PHY 396 T: SUSY Solutions for problem set #12.
|
|
- Juniper Johnston
- 5 years ago
- Views:
Transcription
1 PHY 396 T: SUSY Solutions or problem set #. Problem a: In priniple the non-perturbative superpotential o the theory may depend on the dual quark and antiquark ields q and q as well as the singlets Φ but or simpliity let s ous on the terms whih depend only on the Φ s. In the m 0 limit the theory has anomaly-ree SUN SUN symmetry and the only holomorphi ombination o the Φ ields whih is invariant under this symmetry is the determinant o the Φ matrix. Thereore the non-perturbative superpotential depends on the Φ ields only via the determinant detφ W n.p. Φ λ Λ W n.p. detφ λ Λ. S. To work out the dependene o this superpotential on the Yukawa oupling λ onsider a ield redeinition Φ e t Φ aompanied by the oupling redeinition λ e t λ. In light o equation µ λ 6π N Λ 3N N Λ 3N N /N.5 rom the previous homework set the redeinition o λ leads to µ e t µ and hene µφ µφ whih preserves the duality relation µφ M. Consequently the entire superpotential o the theory inluding both the tree-level and the non-perturbative terms should be invariant under this redeinition. Thereore the Φ ields enter the superpotential only in ombinations λφ Yukawa oupling λ only in ombination λφ hene or µφ. In partiular the W n.p. depends on the Φ and the W n.p. detφ λ Λ W n.p. detλφ Λ. S. Next onsider the axial U symmetry o the theory q e+ia q q e+ia q Φ e ia Φ
2 Θ Θ + N a Λ 3N N e+in a Λ 3N N. S.3 where the seond line ompensates or the axial anomaly. The non-perturbative superpotential should be invariant under this symmetry whih restrit its dependene on the detλφ and the Λ to the invariant ombination detλφ Λ 3N N thus W n.p. Φ λ Λ F detλφ Λ 3N N S.4 or some holomorphi untion F. To ind this untion onsider the anomaly ree R symmetry whose harges you should have ound in problem b o the previous homework: R µ 0 Rgaugino + Rsquark Rantisquark N N Rquark Rantiquark N N S.5 RΦ + N N Rψ φ + N N Rsuperpotential + RΛ 0 where the last line ollows rom the olor anomaly anellation. In partiular detλφ Λ 3N N has R N N N + 0 +N S.6 while F detλφ Λ 3N N should have R +. S.7
3 These R harges immediately imply F detλφ Λ 3N N detλφ Λ 3N N /N a numeri onstant S.8 and hene W n.p. Φ λ Λ detλφ Λ 3N N /N a numeri onstant. For uture reerene I am going to denote this onstant C N. Note: or the problem at hand 3N < N the theory is IR-ree and Λ is the UV Landau pole rather than an IR sale. The irrelevant operators originating at the Λ sale should arry negative powers o Λ and indeed the non-perturbative superpotential arries a negative power o Λ. Problem b: The IR-ree theory does not have a gaugino ondensate and hene does give quantum orretions to the squark-antisquark bilinears M q q. Consequently the bilinear matrix has rank N < N so it annot anel all the O Raieartaigh terms µm. Without the non-perturbative superpotential terms the un-aneled O Raieartaigh terms would lead to spontaneous supersymmetry breaking see arxiv:/hep-th/06039 by Intriligator Seiberg and Shih. On the other hand the dual theory with rankm N has N vaua with S Λ 3N N /N detm M m S 6π. stable supersymmetri S.9 To get similar stable supersymmetri vaua in the theory we need the non-perturbative superpotential. In general hiral VEVs in supersymmetri vaua o any theory ollow rom the onshell hiral ring equations but sine the theory is IR-ree we may use the lassial ield 3
4 equations W net q 0 W net q 0 W net Φ 0. S.0 In partiular the squark obey q Φ 0 Φ q 0 S. so or rank Φ N as we shall see momentarily all squarks and antisquarks have zero VEVs q q 0. s to the Φ ields we have log detλφ Φ Φ S. and hene W n.p. Φ Φ C detλφ Λ 3N N /N. S.3 where C or rather C N o the theory we must have is the numeri onstant in eq.. Thereore in a SUSY vauum Φ CdetλΦ Λ 3N N /N W tree +µm Φ S.4 or equivalently the matrix produt m Φ N N C µ detλφ Λ 3N N /N. S.5 In partiular we must have rankφ N and hene zero squark VEVs. 4
5 To solve the equation S.5 let s take the determinants o both sides o the equation thus hene detm detφ N C detλφ Λ 3N N N /N µ S.6 N N detm] detφ] N C N ] λ N N detφ µ Λ 3N NF ] n S.7 and thereore ] µ N N N N detφ detm µ N Λ N 3N λ N C N N detm] N. S.8 On the right hand side here eq..5 or the µ ator gives us µ N Λ N 3N λ N C N P Λ 3N N S.9 where P N 6π N C N S.0 is a numeri onstant. On the let hand side o S.8 µ N detφ detm det µφ m S. and sine aording to eq. S.5 µφ m is proportional to a unit N N matrix µφ m X N N det µφ m X N. S. Plugging all these ormulae bak into eq. S.8gives us X N N P Λ 3N N detm] N S.3 and hene µ Φ m P Λ 3N N detm] /N. S.4 Comparing this ormula to the eq. S.9 or the meson VEVs o the dual theory we 5
6 immediately see peret agreement between µφ and M up to an overall numeri onstant. Quod erat demonstrandum. PS: To get µφ M without any extra numeri onstants we need P 6π N. S.5 In light o eq. S.0 this alls or C N /N 6π S.6 In other words the non-perturbative superpotential o the theory should be W n.p. N 6π /N det λφ S.7 Λ N 3N with this partiular numeri ator inluding the signs. Problem the exerise part: Consider a dyon in eetive QED whih obtains rom Higgsing o an SU gauge theory by VEV o a salar triplet. I the salars are omplex as in supersymmetri theories their VEVs should have orm Φ a 0 0 eiα v modulo gauge symmetry S.8 or some phase α. In my notations below I assume omplex Φ a although he real salars would an be analyzed in a similar manner. The mass o the dyon omes rom the net energy o the magneti eletri and salar ields thus M dyon d 3 x E a + a + DΦ a + V Φ Φ S.9 where DΦ a are the ovariant spae derivatives o the salars and V Φ Φ V salar Φ Φ V salar vauum. S.30 Note: i V vauum 0 we must subtrat it rom the salar potential so that eq. S.9would 6
7 not mix the energy due to dyons existene with the vauum energy o the theory. Sine salar potential has its minimum in the vauum state the subtrated V Φ Φ is non-negative whih gives us a lower bound or the dyon s mass: M dyon d 3 x E a + a + DΦ a. S.3 In the integrand here E a + a E a + i a S.3 and hene E a + a + DΦ a E a + i a e iβ DΦ a + R e iβ DΦ a E a + i a S.33 or any omplex phase e iβ. The irst term in the RHS is non-negative so the seond term provides us with a lower bound or the LHS. Plugging this bound into the integral in eq. S.3 we arrive at M dyon R e iβ d 3 x DΦ a E a + i a. S.34 Moreover this bound must hold or any phase e iβ whih requires M dyon d 3 x DΦ a E a + i a. S.35. Now let s alulate the integral in this ormula. First let s extrat a total derivative rom the integrand DΦ a E a + i a Φ a E a + i a Φ a D E a + i D a. S.36 In the seond term here we may use the Yang Mills equations or the ovariant divergenes 7
8 o the SU eletri and magneti ields D a 0 D E a J a 0 S.37 where J a µ are the ovariant Yang Mills urrents. ssuming the only soure o these urrents are the salar ields we have J a µ igɛ ab Φ b D µ Φ Φ b D µ Φ. S.38 For a stati oniguration o the salar ields the time omponent µ 0 o this urrent vanishes whih leads to D E a D a 0. S.39 Thus the seond term in eq. S.36 vanishes whih allows us to onvert the spae integral in S.35 to a surae integral at ininite radius d 3 x DΦ a E a + i a d 3 x Φ a E a + i a R drea Φ a E a + i a radial. S.40 Far away rom the monopole the SU eletri and magneti ields are restrited to the unbroken U subgroup o the SU while the salar ields take their vauum values. In the unitary gauge Φ a ve iα 0 0 S.4 while E a + i a E + i EM 0 0. S.4 In other gauges the salar and gauge ields have dierent orms but the produt Φ a E a + i a ve iα E + i EM S.43 8
9 is gauge invariant and have the same orm as in the unitary gauge. Thereore R drea Φ a E a + i a radial ve iα R drea E + i radial EM. S.44 Finally or a dyon with eletri harge Q and magneti harge µ E EM Q n 4πR EM µ n 4πR S.45 and hene drea E + i radial R EM Q + iµ. S.46 Consequently d 3 x DΦ a E a + i a ve iα Q + iµ. S.47 Plugging this integral into the lower bound S.35 or the dyon mass we arrive at the ogomol nyĭ Prasad Sommerield PS bound or the dyon mass: M dyon v Q + iµ. S.48 9
m f f unchanged under the field redefinition (1), the complex mass matrix m should transform into
PHY 396 T: SUSY Solutions or problem set #8. Problem (a): To keep the net quark mass term L QCD L mass = ψ α c m ψ c α + hermitian conjugate (S.) unchanged under the ield redeinition (), the complex mass
More informationGeneralized Gaugino Condensation: Discrete R-Symmetries and Supersymmetric Vacua
Generalized Gaugino Condensation: Discrete R-Symmetries and Supersymmetric Vacua John Kehayias Department of Physics University of California, Santa Cruz SUSY 10 August 23, 2010 Bonn, Germany [1] Generalized
More informationThe Affleck Dine Seiberg superpotential
The Affleck Dine Seiberg superpotential SUSY QCD Symmetry SUN) with F flavors where F < N SUN) SUF ) SUF ) U1) U1) R Φ, Q 1 1 F N F Φ, Q 1-1 F N F Recall that the auxiliary D a fields: D a = gφ jn T a
More informationSupersymmetric Gauge Theories in 3d
Supersymmetric Gauge Theories in 3d Nathan Seiberg IAS Intriligator and NS, arxiv:1305.1633 Aharony, Razamat, NS, and Willett, arxiv:1305.3924 3d SUSY Gauge Theories New lessons about dynamics of quantum
More informationSeiberg Duality: SUSY QCD
Seiberg Duality: SUSY QCD Outline: SYM for F N In this lecture we begin the study of SUSY SU(N) Yang-Mills theory with F N flavors. This setting is very rich! Higlights of the next few lectures: The IR
More informationS-CONFINING DUALITIES
DIMENSIONAL REDUCTION of S-CONFINING DUALITIES Cornell University work in progress, in collaboration with C. Csaki, Y. Shirman, F. Tanedo and J. Terning. 1 46 3D Yang-Mills A. M. Polyakov, Quark Confinement
More informationRectangular Waveguide
0/30/07 EE 4347 Applied Eletromagnetis Topi 5 Retangular Waveguide Leture 5 These notes ma ontain oprighted material obtained under air use rules. Distribution o these materials is stritl prohibited Slide
More informationarxiv:hep-ph/ v1 5 Dec 1996
BUHEP-96-45 hep-ph/96167 A Comment on the Zero Temperature Chiral Phase Transition in SU(N) Gauge Theories arxiv:hep-ph/96167v1 5 De 1996 R. Sekhar Chivukula Department o Physis, Boston University, 590
More informationChapter 11. Maxwell's Equations in Special Relativity. 1
Vetor Spaes in Phsis 8/6/15 Chapter 11. Mawell's Equations in Speial Relativit. 1 In Chapter 6a we saw that the eletromagneti fields E and B an be onsidered as omponents of a spae-time four-tensor. This
More informationFinite Formulation of Electromagnetic Field
Finite Formulation o Eletromagneti Field Enzo TONTI Dept.Civil Engin., Univ. o Trieste, Piazzale Europa 1, 34127 Trieste, Italia. e-mail: tonti@univ.trieste.it Otober 16, 2000 Abstrat This paper shows
More informationNon-Supersymmetric Seiberg duality Beyond the Planar Limit
Non-Supersymmetric Seiberg duality Beyond the Planar Limit Input from non-critical string theory, IAP Large N@Swansea, July 2009 A. Armoni, D.I., G. Moraitis and V. Niarchos, arxiv:0801.0762 Introduction
More informationSinglet-Stabilized Minimal Gauge Mediation
Singlet-Stabilized Minimal Gauge Mediation David Curtin bla arxiv:1011.xxxx In Collaboration with Yuhsin Tsai bla Cornell Institute for High Energy Phenomenology Friday Theory Seminar October 22, 2010
More information(1) For the static field a. = ), i = 0,1,3 ; g R ( R R ) 2 = (2) Here 3 A (3)
Title: The ravitation enery or a ylindrially and spherially symmetrial system Authors: oald Sosnovskiy (Tehnial University, 9, St. Petersbur, ussia It has been shown that t omponent o the enery-momentum
More informationProblem Set 11: Angular Momentum, Rotation and Translation
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department o Physis Physis 80T Fall Term 004 Problem Set : Angular Momentum, Rotation and Translation Available on-line November ; Due: November 3 at 4:00 pm Please
More informationHamiltonian with z as the Independent Variable
Hamiltonian with z as the Independent Variable 1 Problem Kirk T. MDonald Joseph Henry Laboratories, Prineton University, Prineton, NJ 08544 Marh 19, 2011; updated June 19, 2015) Dedue the form of the Hamiltonian
More informationDynamical supersymmetry breaking, with Flavor
Dynamical supersymmetry breaking, with Flavor Cornell University, November 2009 Based on arxiv: 0911.2467 [Craig, Essig, Franco, Kachru, GT] and arxiv: 0812.3213 [Essig, Fortin, Sinha, GT, Strassler] Flavor
More informationGeneration of EM waves
Generation of EM waves Susan Lea Spring 015 1 The Green s funtion In Lorentz gauge, we obtained the wave equation: A 4π J 1 The orresponding Green s funtion for the problem satisfies the simpler differential
More informationPhysics 107 Problem 2.5 O. A. Pringle h Physics 107 Problem 2.6 O. A. Pringle
Pysis 07 Problem 25 O A Pringle 3 663 0 34 700 = 284 0 9 Joules ote I ad to set te zero tolerane ere e 6 0 9 ev joules onversion ator ev e ev = 776 ev Pysis 07 Problem 26 O A Pringle 663 0 34 3 ev
More informationModels of Dynamical Supersymmetry Breaking from a SU(2k+3) Gauge Model* Abstract
SLAC-PUB-7174 hep-th/9605119 May 1996 Models of Dynamical Supersymmetry Breaking from a SU(2k+3) Gauge Model* Chih-Lung Chou Stanford Linear Accelerator Center Stanford University, Stanford, California
More informationVector Field Theory (E&M)
Physis 4 Leture 2 Vetor Field Theory (E&M) Leture 2 Physis 4 Classial Mehanis II Otober 22nd, 2007 We now move from first-order salar field Lagrange densities to the equivalent form for a vetor field.
More informationDynamical SUSY Breaking in Meta-Stable Vacua
UCSD-PTH-06-03 Dynamical SUSY Breaking in Meta-Stable Vacua arxiv:hep-th/0602239v3 1 Apr 2006 Kenneth Intriligator 1,2, Nathan Seiberg 2 and David Shih 3 1 Department of Physics, University of California,
More information4. (12) Write out an equation for Poynting s theorem in differential form. Explain in words what each term means physically.
Eletrodynamis I Exam 3 - Part A - Closed Book KSU 205/2/8 Name Eletrodynami Sore = 24 / 24 points Instrutions: Use SI units. Where appropriate, define all variables or symbols you use, in words. Try to
More informationSinglet-Stabilized Minimal Gauge Mediation
Singlet-Stabilized Minimal Gauge Mediation David Curtin bla arxiv:1011.2766 In Collaboration with Yuhsin Tsai bla Cornell Institute for High Energy Phenomenology Particle Theory Seminar Center for the
More informationNTNU Trondheim, Institutt for fysikk
NTNU Trondheim, Institutt for fysikk Examination for FY3464 Quantum Field Theory I Contact: Michael Kachelrieß, tel. 99890701 Allowed tools: mathematical tables Some formulas can be found on p.2. 1. Concepts.
More informationMetastability. Michael Dine. In collaboration with J. Feng, J. Mason, and E. Silverstein; current collaboration with N. Seiberg
Metastability Michael Dine In collaboration with J. Feng, J. Mason, and E. Silverstein; current collaboration with N. Seiberg In particle physics, we have often considered the possibility that the universe
More informationELECTROMAGNETIC WAVES WITH NONLINEAR DISPERSION LAW. P. М. Меdnis
ELECTROMAGNETIC WAVES WITH NONLINEAR DISPERSION LAW P. М. Меdnis Novosibirs State Pedagogial University, Chair of the General and Theoretial Physis, Russia, 636, Novosibirs,Viljujsy, 8 e-mail: pmednis@inbox.ru
More informationTwo Examples of Seiberg Duality in Gauge Theories With Less Than Four Supercharges. Adi Armoni Swansea University
Two Examples of Seiberg Duality in Gauge Theories With Less Than Four Supercharges Adi Armoni Swansea University Queen Mary, April 2009 1 Introduction Seiberg duality (Seiberg 1994) is a highly non-trivial
More informationv = fy c u = fx c z c The Pinhole Camera Model Camera Projection Models
The Pinhole Camera Model Camera Projetion Models We will introdue dierent amera projetion models that relate the loation o an image point to the oordinates o the orresponding 3D points. The projetion models
More informationVector Mesons and an Interpretation of Seiberg Duality
Vector Mesons and an Interpretation of Seiberg Duality p. 1/?? Vector Mesons and an Interpretation of Seiberg Duality Zohar Komargodski Institute for Advanced Study, Princeton 1010.4105 Vector Mesons and
More informationGreen s function for the wave equation
Green s funtion for the wave equation Non-relativisti ase January 2019 1 The wave equations In the Lorentz Gauge, the wave equations for the potentials are (Notes 1 eqns 43 and 44): 1 2 A 2 2 2 A = µ 0
More information1 Josephson Effect. dx + f f 3 = 0 (1)
Josephson Effet In 96 Brian Josephson, then a year old graduate student, made a remarkable predition that two superondutors separated by a thin insulating barrier should give rise to a spontaneous zero
More informationN =1Supersymmetric Product Group Theories in the Coulomb Phase
hep-th/9704067 MIT-CTP-2622 N =1Supersymmetric Product Group Theories in the Coulomb Phase Csaba Csáki a,1, Joshua Erlich a, Daniel Freedman a,b and Witold Skiba a,2 a Center for Theoretical Physics, Massachusetts
More informationDirac s equation We construct relativistically covariant equation that takes into account also the spin. The kinetic energy operator is
Dira s equation We onstrut relativistially ovariant equation that takes into aount also the spin The kineti energy operator is H KE p Previously we derived for Pauli spin matries the relation so we an
More informationDynamical SUSY Breaking with Anomalous U(1) and the SUSY Flavor Problem
Dynamical SUSY Breaking with Anomalous U(1) and the SUSY Flavor Problem Wang Kai DEPARTMENT OF PHYSICS OKLAHOMA STATE UNIVERSITY In Collaboration with Dr. K.S. Babu and Ts. Enkhbat November 25, 2003 1
More informationFour-dimensional equation of motion for viscous compressible substance with regard to the acceleration field, pressure field and dissipation field
Four-dimensional equation of motion for visous ompressible substane with regard to the aeleration field, pressure field and dissipation field Sergey G. Fedosin PO box 6488, Sviazeva str. -79, Perm, Russia
More informationLagrangian Formulation of the Combined-Field Form of the Maxwell Equations
Physis Notes Note 9 Marh 009 Lagrangian Formulation of the Combined-Field Form of the Maxwell Equations Carl E. Baum University of New Mexio Department of Eletrial and Computer Engineering Albuquerque
More informationExamples of Tensors. February 3, 2013
Examples of Tensors February 3, 2013 We will develop a number of tensors as we progress, but there are a few that we an desribe immediately. We look at two ases: (1) the spaetime tensor desription of eletromagnetism,
More informationELECTROMAGNETIC WAVES
ELECTROMAGNETIC WAVES Now we will study eletromagneti waves in vauum or inside a medium, a dieletri. (A metalli system an also be represented as a dieletri but is more ompliated due to damping or attenuation
More informationusing D 2 D 2 D 2 = 16p 2 D 2
PHY 396 T: SUSY Solutions for problem set #4. Problem (a): Let me start with the simplest case of n = 0, i.e., no good photons at all and one bad photon V = or V =. At the tree level, the S tree 0 is just
More informationExact Solutions of 2d Supersymmetric gauge theories
Exact Solutions of 2d Supersymmetric gauge theories Abhijit Gadde, IAS w. Sergei Gukov and Pavel Putrov UV to IR Physics at long distances can be strikingly different from the physics at short distances
More informationProperties of Quarks
PHY04 Partile Physis 9 Dr C N Booth Properties of Quarks In the earlier part of this ourse, we have disussed three families of leptons but prinipally onentrated on one doublet of quarks, the u and d. We
More informationTENSOR FORM OF SPECIAL RELATIVITY
TENSOR FORM OF SPECIAL RELATIVITY We begin by realling that the fundamental priniple of Speial Relativity is that all physial laws must look the same to all inertial observers. This is easiest done by
More informationHankel Optimal Model Order Reduction 1
Massahusetts Institute of Tehnology Department of Eletrial Engineering and Computer Siene 6.245: MULTIVARIABLE CONTROL SYSTEMS by A. Megretski Hankel Optimal Model Order Redution 1 This leture overs both
More informationFemtosecond laser pulse induced Coulomb explosion
Femtoseond laser pulse indued Coulomb explosion 1 R.ANNOU and V.K.TRIPATHI Physis Department, Indian Institute o Tehnology, New-Delhi 16, INDIA 1 Permanent address: Faulty o physis, University o Sienes
More informationExercise 3: Quadratic sequences
Exerise 3: s Problem 1: Determine whether eah of the following sequenes is: a linear sequene; a quadrati sequene; or neither.. 3. 4. 5. 6. 7. 8. 8;17;3;53;80; 3 p ;6 p ;9 p ;1 p ;15 p ; 1;,5;5;8,5;13;
More informationLecture 15 (Nov. 1, 2017)
Leture 5 8.3 Quantum Theor I, Fall 07 74 Leture 5 (Nov., 07 5. Charged Partile in a Uniform Magneti Field Last time, we disussed the quantum mehanis of a harged partile moving in a uniform magneti field
More informationProblem 1(a): The scalar potential part of the linear sigma model s Lagrangian (1) is. 8 i φ2 i f 2) 2 βλf 2 φ N+1,
PHY 396 K. Solutions for problem set #10. Problem 1a): The scalar potential part of the linear sigma model s Lagrangian 1) is Vφ) = λ 8 i φ i f ) βλf φ N+1, S.1) where the last term explicitly breaks the
More informationSoft Supersymmetry Breaking in
Soft Supersymmetry Breaking in UMD-PP-99-119 SNS-PH/99-12 Deformed Moduli Spaces, Conformal Theories and N = 2 Yang-Mills Theory arxiv:hep-th/9908085v1 11 Aug 1999 Markus A. Luty Department of Physics,
More informationSupersymmetric Gauge Theories, Matrix Models and Geometric Transitions
Supersymmetric Gauge Theories, Matrix Models and Geometric Transitions Frank FERRARI Université Libre de Bruxelles and International Solvay Institutes XVth Oporto meeting on Geometry, Topology and Physics:
More informationDynamics of the Electromagnetic Fields
Chapter 3 Dynamis of the Eletromagneti Fields 3.1 Maxwell Displaement Current In the early 1860s (during the Amerian ivil war!) eletriity inluding indution was well established experimentally. A big row
More informationThe Corpuscular Structure of Matter, the Interaction of Material Particles, and Quantum Phenomena as a Consequence of Selfvariations.
The Corpusular Struture of Matter, the Interation of Material Partiles, and Quantum Phenomena as a Consequene of Selfvariations. Emmanuil Manousos APM Institute for the Advanement of Physis and Mathematis,
More informationHOW TO FACTOR. Next you reason that if it factors, then the factorization will look something like,
HOW TO FACTOR ax bx I now want to talk a bit about how to fator ax bx where all the oeffiients a, b, and are integers. The method that most people are taught these days in high shool (assuming you go to
More informationParticle-wave symmetry in Quantum Mechanics And Special Relativity Theory
Partile-wave symmetry in Quantum Mehanis And Speial Relativity Theory Author one: XiaoLin Li,Chongqing,China,hidebrain@hotmail.om Corresponding author: XiaoLin Li, Chongqing,China,hidebrain@hotmail.om
More informationUV Completions of Composite Higgs Models with Partial Compositeness
UV Completions of Composite Higgs Models with Partial Compositeness Marco Serone, SISSA, Trieste Based on 1211.7290, in collaboration with Francesco Caracciolo and Alberto Parolini and work in progress
More informationCasimir self-energy of a free electron
Casimir self-energy of a free eletron Allan Rosenwaig* Arist Instruments, In. Fremont, CA 94538 Abstrat We derive the eletromagneti self-energy and the radiative orretion to the gyromagneti ratio of a
More informationn n=1 (air) n 1 sin 2 r =
Physis 55 Fall 7 Homework Assignment #11 Solutions Textbook problems: Ch. 7: 7.3, 7.4, 7.6, 7.8 7.3 Two plane semi-infinite slabs of the same uniform, isotropi, nonpermeable, lossless dieletri with index
More informationAnswers to test yourself questions
Answers to test yoursel questions Topi.1 Osilliations 1 a A n osillation is any motion in whih the displaement o a partile rom a ixed point keeps hanging diretion and there is a periodiity in the motion
More informationProblem 1(a): At equal times or in the Schrödinger picture the quantum scalar fields ˆΦ a (x) and ˆΠ a (x) satisfy commutation relations
PHY 396 K. Solutions for homework set #7. Problem 1a: At equal times or in the Shrödinger iture the quantum salar fields ˆΦ a x and ˆΠ a x satisfy ommutation relations ˆΦa x, ˆΦ b y 0, ˆΠa x, ˆΠ b y 0,
More informationSingle-sector supersymmetry breaking, chirality and unification
SLAC-PUB-1447 Single-sector supersymmetry breaking, chirality and unification Siavosh R. Behbahani a,b, Nathaniel Craig b,c,d, Gonzalo Torroba a,b a SLAC National Accelerator Laboratory, Stanford, CA 94309
More informationLecture 12 Holomorphy: Gauge Theory
Lecture 12 Holomorphy: Gauge Theory Outline SUSY Yang-Mills theory as a chiral theory: the holomorphic coupling and the holomorphic scale. Nonrenormalization theorem for SUSY YM: the gauge coupling runs
More informationIntroduction to Supersymmetry
Introduction to Supersymmetry I. Antoniadis Albert Einstein Center - ITP Lecture 5 Grand Unification I. Antoniadis (Supersymmetry) 1 / 22 Grand Unification Standard Model: remnant of a larger gauge symmetry
More information(a) We desribe physics as a sequence of events labelled by their space time coordinates: x µ = (x 0, x 1, x 2 x 3 ) = (c t, x) (12.
2 Relativity Postulates (a) All inertial observers have the same equations of motion and the same physial laws. Relativity explains how to translate the measurements and events aording to one inertial
More informationNon-Markovian study of the relativistic magnetic-dipole spontaneous emission process of hydrogen-like atoms
NSTTUTE OF PHYSCS PUBLSHNG JOURNAL OF PHYSCS B: ATOMC, MOLECULAR AND OPTCAL PHYSCS J. Phys. B: At. Mol. Opt. Phys. 39 ) 7 85 doi:.88/953-75/39/8/ Non-Markovian study of the relativisti magneti-dipole spontaneous
More information+ µ 2 ) H (m 2 H 2
I. THE HIGGS POTENTIAL AND THE LIGHT HIGGS BOSON In the previous chapter, it was demonstrated that a negative mass squared in the Higgs potential is generated radiatively for a large range of boundary
More informationGreen s function for the wave equation
Green s funtion for the wave equation Non relativisti ase 1 The wave equations In the Lorentz Gauge, the wave equations for the potentials in Lorentz Gauge Gaussian units are: r 2 A 1 2 A 2 t = 4π 2 j
More informationVacuum Energy and Effective Potentials
Vacuum Energy and Effective Potentials Quantum field theories have badly divergent vacuum energies. In perturbation theory, the leading term is the net zero-point energy E zeropoint = particle species
More informationAdvanced Computational Fluid Dynamics AA215A Lecture 4
Advaned Computational Fluid Dynamis AA5A Leture 4 Antony Jameson Winter Quarter,, Stanford, CA Abstrat Leture 4 overs analysis of the equations of gas dynamis Contents Analysis of the equations of gas
More informationAharonov-Bohm effect. Dan Solomon.
Aharonov-Bohm effet. Dan Solomon. In the figure the magneti field is onfined to a solenoid of radius r 0 and is direted in the z- diretion, out of the paper. The solenoid is surrounded by a barrier that
More informationQUANTUM MECHANICS II PHYS 517. Solutions to Problem Set # 1
QUANTUM MECHANICS II PHYS 57 Solutions to Problem Set #. The hamiltonian for a lassial harmoni osillator an be written in many different forms, suh as use ω = k/m H = p m + kx H = P + Q hω a. Find a anonial
More informationarxiv:gr-qc/ v2 6 Feb 2004
Hubble Red Shift and the Anomalous Aeleration of Pioneer 0 and arxiv:gr-q/0402024v2 6 Feb 2004 Kostadin Trenčevski Faulty of Natural Sienes and Mathematis, P.O.Box 62, 000 Skopje, Maedonia Abstrat It this
More informationLet s move to Bound States
Let s move to Bound States When we disuss bound states of two objets in entral-fore potential, kineti energy and potential energy are ~the same. How does this ompare to the rest energy of the objets? Hydrogen
More informationMetastable supersymmetry breaking and multitrace deformations of SQCD
February 2009 RUNHETC-2008-20, SLAC-PUB-13467 NSF-KITP-08-143, MIFP-08-28 Metastable supersymmetry breaking and multitrace deformations of SQCD Rouven Essig 1, Jean-François Fortin 2, Kuver Sinha 3, Gonzalo
More informationBrazilian Journal of Physics, vol. 29, no. 3, September, Classical and Quantum Mechanics of a Charged Particle
Brazilian Journal of Physis, vol. 9, no. 3, September, 1999 51 Classial and Quantum Mehanis of a Charged Partile in Osillating Eletri and Magneti Fields V.L.B. de Jesus, A.P. Guimar~aes, and I.S. Oliveira
More informationLecture 7: N = 2 supersymmetric gauge theory
Lecture 7: N = 2 supersymmetric gauge theory José D. Edelstein University of Santiago de Compostela SUPERSYMMETRY Santiago de Compostela, November 22, 2012 José D. Edelstein (USC) Lecture 7: N = 2 supersymmetric
More informationField and Wave Electromagnetic
Field and Wave Eletromagneti Chapter Waveguides and Cavit Resonators Introdution () * Waveguide - TEM waves are not the onl mode o guided waves - The three tpes o transmission lines (parallel-plate, two-wire,
More informationLecture 5 The Renormalization Group
Lecture 5 The Renormalization Group Outline The canonical theory: SUSY QCD. Assignment of R-symmetry charges. Group theory factors: bird track diagrams. Review: the renormalization group. Explicit Feynman
More informationSUSY QCD. Consider a SUSY SU(N) with F flavors of quarks and squarks
SUSY gauge theories SUSY QCD Consider a SUSY SU(N) with F flavors of quarks and squarks Q i = (φ i, Q i, F i ), i = 1,..., F, where φ is the squark and Q is the quark. Q i = (φ i, Q i, F i ), in the antifundamental
More informationSolutions to gauge hierarchy problem. SS 10, Uli Haisch
Solutions to gauge hierarchy problem SS 10, Uli Haisch 1 Quantum instability of Higgs mass So far we considered only at RGE of Higgs quartic coupling (dimensionless parameter). Higgs mass has a totally
More informationVelocity Addition in Space/Time David Barwacz 4/23/
Veloity Addition in Spae/Time 003 David arwaz 4/3/003 daveb@triton.net http://members.triton.net/daveb Abstrat Using the spae/time geometry developed in the previous paper ( Non-orthogonal Spae- Time geometry,
More informationThe homopolar generator: an analytical example
The homopolar generator: an analytial example Hendrik van Hees August 7, 214 1 Introdution It is surprising that the homopolar generator, invented in one of Faraday s ingenious experiments in 1831, still
More informationPrarit Agarwal (Seoul National University) International winter school : "Partition Functions and Automorphic Forms", 2018
Prarit Agarwal (Seoul National University) International winter school : "Partition Functions and Automorphic Forms", 2018 Based on 1. N=1 Deformations and RG Flows of N=2 SCFTs - J. Song, K. Maruyoshi
More informationTextbook Problem 4.2: We begin by developing Feynman rules for the theory at hand. The Hamiltonian clearly decomposes into Ĥ = Ĥ0 + ˆV where
PHY 396 K. Solutions for problem set #11. Textbook Problem 4.2: We begin by developing Feynman rules for the theory at hand. The Hamiltonian clearly decomposes into Ĥ = Ĥ0 + ˆV where Ĥ 0 = Ĥfree Φ + Ĥfree
More informationRoni Harnik LBL and UC Berkeley
Roni Harnik LBL and UC Berkeley with Daniel Larson and Hitoshi Murayama, hep-ph/0309224 Supersymmetry and Dense QCD? What can we compare b/w QCD and SQCD? Scalars with a chemical potential. Exact Results.
More informationControl of industrial robots. Control of the interaction
Control o industrial robots Control o the interation Pro. Paolo Roo (paolo.roo@polimi.it) Politenio di Milano Dipartimento di Elettronia, Inormazione e Bioingegneria Introdution So ar we have assumed that
More information11 Radiation in Non-relativistic Systems
Radiation in Non-relativisti Systems. Basi equations This first setion will NOT make a non-relativisti approximation, but will examine the far field limit. (a) We wrote down the wave equations in the ovariant
More informationNonperturbative Study of Supersymmetric Gauge Field Theories
Nonperturbative Study of Supersymmetric Gauge Field Theories Matteo Siccardi Tutor: Prof. Kensuke Yoshida Sapienza Università di Roma Facoltà di Scienze Matematiche, Fisiche e Naturali Dipartimento di
More informationSpinning Charged Bodies and the Linearized Kerr Metric. Abstract
Spinning Charged Bodies and the Linearized Kerr Metri J. Franklin Department of Physis, Reed College, Portland, OR 97202, USA. Abstrat The physis of the Kerr metri of general relativity (GR) an be understood
More informationEmbedding the Pentagon
Preprint typeset in JHEP style - PAPER VERSION hep-th07 scipp-07/13 Embedding the Pentagon arxiv:0708.0022v2 [hep-th] 26 Sep 2007 T. Banks Department of Physics University of California, Santa Cruz, CA
More informationF = F x x + F y. y + F z
ECTION 6: etor Calulus MATH20411 You met vetors in the first year. etor alulus is essentially alulus on vetors. We will need to differentiate vetors and perform integrals involving vetors. In partiular,
More informationPractice Exam 2 Solutions
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department o Physis Physis 801T Fall Term 004 Problem 1: stati equilibrium Pratie Exam Solutions You are able to hold out your arm in an outstrethed horizontal position
More informationELECTROMAGNETIC NORMAL MODES AND DISPERSION FORCES.
ELECTROMAGNETIC NORMAL MODES AND DISPERSION FORCES. All systems with interation of some type have normal modes. One may desribe them as solutions in absene of soures; they are exitations of the system
More informationPREDICTION OF CONCRETE COMPRESSIVE STRENGTH
PREDICTION OF CONCRETE COMPRESSIVE STRENGTH Dunja Mikuli (1), Ivan Gabrijel (1) and Bojan Milovanovi (1) (1) Faulty o Civil Engineering, University o Zagreb, Croatia Abstrat A ompressive strength o onrete
More informationThe gravitational phenomena without the curved spacetime
The gravitational phenomena without the urved spaetime Mirosław J. Kubiak Abstrat: In this paper was presented a desription of the gravitational phenomena in the new medium, different than the urved spaetime,
More informationAnomaly and gaugino mediation
Anomaly and gaugino mediation Supergravity mediation X is in the hidden sector, P l suppressed couplings SUSY breaking VEV W = ( W hid (X) + W vis ) (ψ) f = δj i ci j X X ψ j e V ψ 2 i +... Pl τ = θ Y
More informationInverse See-saw in Supersymmetry
Inverse See-saw in Supersymmetry Kai Wang IPMU, the University of Tokyo Cornell Particle Theory Seminar September 15, 2010 hep-ph/10xx.xxxx with Seong-Chan Park See-saw is perhaps the most elegant mechanism
More informationthe following action R of T on T n+1 : for each θ T, R θ : T n+1 T n+1 is defined by stated, we assume that all the curves in this paper are defined
How should a snake turn on ie: A ase study of the asymptoti isoholonomi problem Jianghai Hu, Slobodan N. Simić, and Shankar Sastry Department of Eletrial Engineering and Computer Sienes University of California
More informationSupersymmetry Breaking 1
Supersymmetry Breaking 1 Yael Shadmi arxiv:hep-th/0601076v1 12 Jan 2006 Physics Department, Technion Israel Institute of Technology, Haifa 32000, Israel yshadmi@physics.technion.ac.il Abstract These lectures
More informationdepend on the renormalization sheme) only near the ritial point at zero oupling while at intermediate and strong ouplings this statement is still ques
ASYMMETRY PARAMETER ROLE IN DESCRIPTION OF PHASE STRUCTURE OF LATTICE GLUODYNAMICS AT FINITE TEMPERATURE. L. A. Averhenkova, K. V. Petrov, V. K. Petrov, G. M. Zinovjev Bogolyubov Institute for Theoretial
More informationNTNU Trondheim, Institutt for fysikk
FY3464 Quantum Field Theory II Final exam 0..0 NTNU Trondheim, Institutt for fysikk Examination for FY3464 Quantum Field Theory II Contact: Kåre Olaussen, tel. 735 9365/4543770 Allowed tools: mathematical
More informationSUSY N=1 ADE Dynamics
SUSY N=1 ADE Dynamics DK, J. Lin arxiv: 1401.4168, 1402.5411 See also J. Lin s talk IntroducJon In the last twenty years there has been important progress in supersymmetric field theory. At the same Jme,
More information