Supersymmetric Skyrme Model. Muneto Nitta (Keio U.,Jp)
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1 Supersymmetric Skyrme Model June Krakow SIG V June 2016: Skyrmions - from atomic nuclei to neutron stars Muneto Nitta (Keio U.,Jp) Shin Sasaki (Kitasato U., Jp) Sven Bjarke Gudnason (Lanzhou, China)
2 Refs [1] MN, S.Sasaki, Phys.Rev. D90 (2014) [arxiv: [hep-th]] [2] MN, S.Sasaki, Phys.Rev. D90 (2014) [arxiv: [hep-th]] [3] MN, S.Sasaki, Phys.Rev. D91 (2015) [arxiv: [hep-th]] [4] S.B. Gudnason, MN, S.Sasaki, JHEP 1602 (2016) 074 [arxiv: [hep-th]] [5] MN, Mod.Phys.Lett. A15 (2000) [hep-th/ ]
3 Keio Yokohama in greater Tokyo Topological Science Project Aimed to understand all subjects of physics in terms of Topology 5 years, 11 postdocs Anyone here is very welcome to visit!!
4 Motivation Skyrme model: Skyrme( 61) Low-energy effective theory(leet) of QCD Bayons = Solitons (Skyrmions) LEET of N=1, N=2 SUSY QCD ( 90s --) Exact results Seiberg, Seiberg-Witten ( 94) LEET of SUSY QCD in chiral symm breaking sector SUSY extension of Skyrme model SUSY Skyrmions = SUSY baryons? Exact? Notorious Problem in SUSY higher derivatives Progress in baby-skyrme model by Adam, Queiruga, Sanchez-Guillen, Wereszczynski ( 12-)
5 Motivation Low-energy effective theories are usually derivative expansion. Chiral Lagrangian, SUGRA as low-energy string etc 1. LEEA of SUSY field theories: Derivative corrections in LEEA, SUGRA 2. SUSY extension of HD theories Chiral Lagrangian, Wess-Zumino-Witten, Skyrme model, Faddeev-Skyme model 3. LEET of BPS p-branes, BPS topological solitons: Dirac-Born-Infeld, Nambu-Goto etc 4. Cosmology: k-inflation, Galileon inflation, ghost condensate
6 Notorious Problem: Auxiliary Field Problem Chiral superfield y m x m i m Auxliary field ( y, ) ( y) ( y) F( y) H.D terms acts on In general, F cannot be eliminated algebraically. F may become dynamical DOF. Is SUSY OK? Introduce of further fermion partner? Is it always the case? If not, how can we construct higher derivative term without this problem? m
7 SUSY Wess-Zumino-Witten term Nemechansky & Rohm( 85) i d Nucl. Phys. B249, 157 (1985). 4 i m j (, ) D k m D ijk (2,1) tensor If one sets F 0 c.c. WZW Additional However, explicitly MN( 00)
8 SUSY Faddeev-Skyrme term CP 1 model + 4 deriv d D 4 i D j D i D Nucl. Phys. B249, 93 (1985). Bergshoeff,Nepomechie&Schnitzer( 85) j d D 4 D i D D i mf but put F 0 L. Freyhult, Nucl. Phys. B681, 65 (2004). 4 t 1. 4 deriv term must contain ---- no Hamiltonian (Skyrme term deos not) 2. One cannot introduce superpotential W 3. is a solution, but dynamical? Quantization? F 0
9 The unique term free from the AF problem found so far d 4 ikjl ikjl (, ) D D D D i k j l (2,2) tensor 4 derivative term I.L. Buchbinder, S. Kuzenko, and Z. Yarevskaya, NPB411, 665 (1994) A. T. Banin, I. L. Buchbinder, and N. G. Pletnev, PRD74, (2006) J. Khoury, J.-L. Lehners, and B. Ovrut, PRD83, (2011) J. Khoury, J.-L. Lehners, and B. Ovrut, PRD84, (2011) M. Koehn, J.-L. Lehners, and B. A. Ovrut, PRD86, (2012) C. Adam, J.M. Queiruga, J. Sanchez-Guillen, and A.Wereszczynski, JHEP05 (2013)108 C. Adam, J.M. Queiruga, J. Sanchez-Guillen, and A.Wereszczynski, Phys. Rev. D 86, (2012) S. Sasaki, M. Yamaguchi, and D. Yokoyama, PLB718, 1(2012) LEEA of susy WZW Ghost condensate Galileon SUGRA SUSY baby Skyrmion SUSY k-field theory suerpotential
10 The unique term free from the AF problem found so far d 4 ikjl ikjl (, ) D D i k j D D l (2,2) tensor 4 derivative term ikjl can contain derivatives too: ikjl (,, m, m ) Derivatives more than 4 Can be used to construct derivative corrections to arbitrary order MN, S.Sasaki, Phys.Rev. D90 (2014) [arxiv: [hep-th]]
11 BPS lumps & baby Skyrmions MN, S.Sasaki, Phys.Rev. D90 (2014) [arxiv: [hep-th]]
12 Bosonic part No derivative on F EOM
13 EOM For W 0, F 0 We call this canonical branch is one solution But this is not so good, because it contains t (Skyrme term, Faddeev-Skyrme term do not.) Cannot be applied for W 0, For a single component, we can go further! (Multi-component is still difficult.) 4
14 EOM for a single component W 0 Canonical branch 4 t Non-canonical branch Baby Skyrme without t No usual kinetic term 4 Potential even without W
15 Remarks on non-canonical branch No 0 limit, because of the potential. 0 for consistency. K does not have a meaning of the Kahler metric. SUSY baby Skyrme model for CP 1 C. Adam, J.M. Queiruga, J. Sanchez-Guillen, and A. Wereszczynski, J. High Energy Phys. 05 (2013) 108.
16 EOM for a single component W 0 3 solutions (branches)
17 SUSY transformation Conditions on BPS equations BPS lumps ½ SUSY 1 0 On-shell BPS equation cancelled out Bogomol nyi bound (the same with = 0) z ( x ix ) 1 i ( M ) Ζ
18 BPS baby Skyrmion ¼ SUSY Off-shell BPS equation On-shell BPS equation Same with d.w.junction Bogomol nyi bound + ( ) Ζ 2 M Compacton Adam et.al The same with ½ BPS lump
19 SUSY Skyrme model S.B. Gudnason, MN, S.Sasaki, JHEP 1602 (2016) 074 [arxiv: [hep-th]]
20 Chiral symmetry breaking Nambu-Goldstone(NG) boson (pions) U e i A TA Complexified for N=1 SUSY Not Kahler NG Quasi-NG
21 W. Lerche, NPB238(1984)582 G.M. Shore, NPB248(1984)123 Theorem (Lerche, Shore 84 ) 1. There must appear at least one QNG boson for symmetry breaking with preserving SUSY (in the absence of gauge interaction). 2. For real representation, the same number of QNG bosons as the number of NG bosons appear (fully doubled). (eg: chiral symmetry breaking)
22 G-transformation law The most general G-invariant Kahler potential The simplest G.M.Shore( 89) Setting QNG=0 Usual principal chiral model
23 SUSY Skyrme term Bosonic part Canonical branch F 0 including t 4 Not Skyrme term
24 Non-canonical branch (SU(2)) Setting QNG=0 without t 4 Skyrme term!!
25 Inclusion of Kahler potential Setting QNG=0 Skyrme term No usual kinetic term Potential term
26 Summary 1. SUSY baby Skyrme model 2. SUSY Skyrme model 3. (Higher derivative terms without the auxiliary field problem) 4. (Classified BPS equations) Future works 1. BPS Skyrmions in the SUSY Skyrme model? 2. Inclusion of superpotential 3. N =2 SUSY extension 4. Can t we really introduce usual kinetic term? 5. LEET of SUSY QCD? SUSY WZW? 6. SUSY extension of BPS Skyrme model?
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