Brane SUSY Breaking, non-linear SUSY and Some Applications

Transcription

1 Brane SUSY Breaking, non-linear SUSY and Some Applications Augusto Sagnotti Scuola Normale Superiore and INFN Pisa TFI 2017 Theories of the Fundamental Interactions Parma, September

2 10D Superstrings And Brane SUSY Breaking 2

3 Ten-Dimensional (Closed) Superstrings Building principles of (closed) string spectra and the vacuum energy: spin-statistics (GSO projections) modular invariance (Gliozzi, Scherk, Olive, 1977) IIA, IIB: HE, HO: SUSY: 0A, 0B: H 16x16 : (Dixon, Harvey, 1986) 3 (Alvarez-Gaumé, Ginsparg, Moore, Vafa, 1986)

4 Open Descendants, or Orientifolds (AS, 1987) Models with OPEN strings DESCEND from closed ones via orientifold projections. In particular: the SO(32) type-i superstring descends from type-iib MIX L and R string MODES (+ M. Bianchi, G. Pradisi, ; D. Fioravanti, 1993; Y. Stanev, 1994-) New 2D ingredients: RR tadpole(s): neutrality conditions The procedure fills vacua with D-branes and O-planes (Polchinski, 1995) 4

5 10D Tachyon-Free Orientifolds 1) SO(32) type-i: in vacuum BPS combination (O - orientifold (T<0,Q<0) and D-branes (T>0,Q>0)). Massless Weyl fermions in the adjoint of SO(32) D-branes T>0, Q>0 O- T<0, Q<0 5

6 10D Tachyon-Free Orientifolds 1. U(32) type-0 b: [NO SUSY, T > 0 ] (AS, 1995) 2. USp(32) type-i: [non-linear SUSY, T > 0 ] (Sugimoto, 1999) D- antibranes T>0, Q<0 O+ T>0, Q>0 Only sign of V flipped w.r.t. type- I SO(32)! 6

7 Brane SUSY Breaking (BSB) (Sugimoto, 1999) (Antoniadis, Dudas, AS, 1999) (Angelantonj, 1999) (Aldazabal, Uranga, 1999) Tree level SUSY broken at string scale in open sector, exact in closed sector Stable vacuum (classically) Goldstino in open sector BSB: Tension unbalance critical exponential (runaway) potential [ SAME exponential (from D anti D): KKLT uplift (2003), or in U(32) orientifold] [ SIMILAR exponential potential: from torus correction in SO(16) x SO(16) heterotic] 7

8 Some Lessons from the (BSB) Runaway Potential 8

9 Low-Energy Lagrangians Three 10D tachyon-free string models: In string frame (T Λ for heterotic): - BSB Usp(32) ORIENTIFOLD [NON-LINEAR SUSY] - 0B U(32) ORIENTIFOLD [ NO SUSY] - Heterotic SO(16) x SO(16) [NO SUSY] In Einstein frame (T Λ for heterotic): Here: Orientifolds: Heterotic: 9

10 BSB: a 9D Vacuum (Dudas, and Mourad, 2000, 2001) 1. 9D solution that (in string frame) describes an S 1 /Z 2 (interval) compactification. Finite 9D Planck mass and gauge coupling, but singularities at the ends [ similar, albeit more complicated looking, results also for heterotic SO(16) x SO(16) ] HOWEVER: two kinds of problems with this solution: a) string loop corrections: determined by the second equation, grow out of control for y ; b) curvature corrections: large near y=0. 10

11 BSB: (Pre)Inflation with a bounce? (Dudas, Kitazawa, AS, 2010) 1. Critical tadpole exponent: precisely at the onset of the climbing phenomenon. (Lucchin, Matarrese, 1985) (Halliwell, 1987) (Dudas, Mourad, 2000) (Russo, 2004) (Dudas, Kitazawa, AS, 2010) 2. Scalar emerges from initial singularity climbing up ANY potential that corrects BSB by softer terms. Now: bounded string loop corrections [NOT SO curvature corrections, however] 3. Slow-roll after bounce and deceleration: Last stages of deceleration imprinted in CMB? Low-l lack of power [& Low-l enhancement of tensor-to-scalar ratio r]. 11

12 (Pre-)Inflation with a Bounce (Dudas, Kitazawa, AS, 2010) (Dudas, Kitazawa, Patil, AS, 2012) E.g. : 1) Low-l lack of power in CMB from a decelerating inflaton? (& possibly low-l increase of tensor-to-scalar ratio) IF WE WERE TO ACCESS, via the CMB, to the onset of slow roll ΛCDMΔ 2) PLANCK 2015 (high latitudes): (Gruppuso, Mandolesi, Natoli, Kitazawa, AS, 2015) 12

13 Pre-Inflationary Relics in the CMB? Extend ΛCDM to allow for low-l suppression: (Gruppuso, Mandolesi, Natoli, Kitazawa, AS, 2015) NO effects on standard ΛCDM parameters (6+16 nuisance) A new scale. Preferred value? Depends on GALACTIC MASK. What is the corresponding energy scale at onset of inflation? 13

14 Non-Singular (Flux) Vacuum Configurations 1) The class of metrics: 2) Constant dilaton profiles : aim at fixing the dilaton, despite the runaway potentials 3) Vacuum configurations for : CFT analysis: (charged and uncharged) brane configurations for these orientifold systems. [Around the flat space empty vacuum (ignoring the dilaton tadpole)] (Dudas, Mourad, AS, 2001) HOW will the CFT analysis connect to the actual deformed backgrounds? 14

15 Orientifold (Flux) Vacua with BSB (Mourad, AS, 2016) In this fashion the field equations reduce to ( ): Dilaton eq: strong constraint due to positivity of l.h.s. (β E < 0 for orientifolds & T>0, NEED H 3 fluxes) First two eqs: determine k =1 (internal sphere), and its radius R=e C and φ in terms of h Third eq: determines for k=0 A ~r, and thus AdS in Poincaré coordinates (or in other slicings for k 0) 15

16 AdS Slicings Let us take a closer look at the last equation: It is solved by: These metrics emerge from three different slicing of the same AdS space, for which 1. K = 1 slicing: 2. K=-1 slicing: 3. K=0 slicing: 16

17 AdS 3 x S 7 (Flux) Orientifold Vacua ( ) This family of solutions: exists only for T 0 includes a perturbative corner (large R, small g s ) [reasons to expect that one is solving the complete string equations] accommodates a residual unbroken gauge group (Usp(32) or U(32)) This special class of vacua appears PERTURBATIVELY STABLE (I. Basile, J. Mourad, AS, in progress) (I. Basile, Master s Thesis, Sept. 2017) NON - PERTURBATVELY? 17

18 Constrained Superfields and 4D Models 18

19 BSB: 10D non-linear supergravity PROBLEM: couple a Volkov-Akulov-like goldstino to 10D Supergravity (+YM), ADAPTING (Dudas, Mourad, 2001) (Pradisi, Riccioni, 2001) (Akulov, Volkov, 1973) (Off-shell) 4D SUSY transformations on the goldstino can be induced, by analogy, from superspace shifts: SUSY transformations: act as special diffeomorphisms on Invariant (flat) goldstino action: Can extend the methods for coupling to 4D supergravity, extending the work in and then, in 10D: (Samuel, Wess, 1973) All orders in fermions? Complicated since transformations are redefined (Bonnefoy, Dudas, Mourad, in progress) 19

20 Constrained Superfields in D=4 Consider an O(N) invariant scalar model: For λ : a σ-model describing the dynamics in the valley of minima In the Wess-Zumino multiplet of 4D SUSY, when the scalar becomes very massive For λ : a fermion with broken SUSY. Volkov-Akulov (1973) model (up to field redefinitions) (Casalbuoni, De Curtis, Dominici, Feruglio, Gatto, 1989) (Komargodski, Seiberg, 2009) Several N=1 N=0 constraints were investigated in recent years (see talk by N. Cribiori). 20

21 4D Supergravity with Constrained Superfields Constrained superfields: a powerful and instructive tool in Supergravity they allow to resort directly to the general N=1 expression for the potential while enforcing in it the constraints. Simple to build interesting examples: NO extra fields Example 1 (Volkov-Akulov supergravity): (X 2 =0) (Antoniadis, Dudas, Ferrara, AS, 2014) (Dudas, Ferrara, Kehagias, AS, 2015) (Bergshoeff, Freedman, Kallosh, Van Proeyen, 2015) (Antoniadis, Markou, 2015) Example 2 (Volkov-Akulov-Starobinsky supergravity): (X 2 =0, with some redefinitions) Important additions by many authors: exit from inflation, other cosmological models, [ BSB: ] (Ferrara, Kallosh, Linde, 2014) (Dall Agata, Zwirner, 2014) (Bergshoeff, Freedman, Kallosh, Van Proeyen, 2015) (Antoniadis, Markou, 2015). 21

22 4D Toy Models with Constrained Superfields (BPS-like: 2 1 breaking) N=2 vector multiplet (1 vector + 1 chiral multiplet in N=1 language): one can consider the decoupling limit for a very massive chiral multiplet partial breaking N=2 N=1 occurs, with magnetic coupling m non-linear constraint: (Bagger, Galperin, 1997) (Rocek, Tseytlin, 1999). (Hughes, (Liu), Polchinski, 1986) (Antoniadis, Partouche, Taylor, 1996) (Ferrara, Girardello, Porrati, 1996) in N=2 language: highest component yields SUSY Born-Infeld theory: can extend to a number n of abelian vector multiplets: (Ferrara, Porrati, AS, 2014) (Ferrara, Porrati, AS, Stora, Yeranyan, 2014) Microscopically: toy models for separated D-branes. Non-Abelian lessons? 22

23 4D Models with Constrained Superfields (BSB-like: 2 0 breaking) N=2 vector multiplet (1 vector + 1 chiral multiplet in N=1 language): one can consider a different decoupling limit, leaving behind a vector and two goldstini non-linear constraint: (Dudas, Ferrara, AS, 2017) In N=2 language: Away from a singular 2 1 corner: complex scalar in terms of the vector and gaugini 23

24 Thank You 24

25 Before Closing... On June 9 Yassen STANEV left us after a brief illness. Yassen had studied in Sofia, with Ivan TODOROV, in a group has contributed significantly, over the years, to Quantum Field Theory. He had joined the Tor Vergata Theory Group in 1994, and after a few years was hired by INFN as Primo Ricercatore. During the last years he had also represented the Tor Vergata group in the INFN Theoretical Physics Committee. Yassen was a high-class expert in Conformal Field Theory, a subject to which he had contributed since his student days. I had the privilege of working intensely with Yassen (and with Gianfranco PRADISI) in , on 2D boundary CFT, and then (also with Carlo ANGELANTONJ, Massimo BIANCHI and, in part, with Sergio FERRARA) on open-string compactifications. In the following years Yassen worked successfully on a number of topics connected with the AdS/CFT correspondence. His last work, with several colleagues at Tor Vergata and Torino, has appeared after his untimely death. We miss his wit, his sense of humor, his uncommon technical skills, his critical views and his friendship 25