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Title: Spontaneous Z{sub 2} symmetry breaking in the orbifold daughter of N=1 super-Yang-Mills theory, fractional domain walls and vacuum structure

Abstract

We discuss the fate of the Z{sub 2} symmetry and the vacuum structure in a SU(N)xSU(N) gauge theory with one bifundamental Dirac fermion. This theory can be obtained from SU(2N) supersymmetric Yang-Mills theory by virtue of Z{sub 2} orbifolding. We analyze dynamics of domain walls and argue that the Z{sub 2} symmetry is spontaneously broken. Since unbroken Z{sub 2} is a necessary condition for nonperturbative planar equivalence we conclude that the orbifold daughter is nonperturbatively nonequivalent to its supersymmetric parent. En route, our investigation reveals the existence of fractional domain walls, similar to fractional D-branes of string theory on orbifolds. We conjecture on the fate of these domain walls in the true solution of the Z{sub 2}-broken orbifold theory. We also comment on relation with nonsupersymmetric string theories and closed-string tachyon condensation.

Authors:
 [1];  [2];  [3];  [2]
  1. Department of Physics, University of Wales Swansea, Singleton Park, Swansea, SA2 8PP (United Kingdom)
  2. William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455 (United States)
  3. (Russian Federation)
Publication Date:
OSTI Identifier:
20711580
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 72; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.72.105001; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; GAUGE INVARIANCE; MATHEMATICAL SOLUTIONS; MEMBRANES; QUANTUM FIELD THEORY; STRING MODELS; SU GROUPS; SUPERSYMMETRY; SYMMETRY BREAKING; VACUUM STATES; YANG-MILLS THEORY

Citation Formats

Armoni, A., Gorsky, A., Institute of Theoretical and Experimental Physics, Moscow 117259, and Shifman, M.. Spontaneous Z{sub 2} symmetry breaking in the orbifold daughter of N=1 super-Yang-Mills theory, fractional domain walls and vacuum structure. United States: N. p., 2005. Web. doi:10.1103/PhysRevD.72.105001.
Armoni, A., Gorsky, A., Institute of Theoretical and Experimental Physics, Moscow 117259, & Shifman, M.. Spontaneous Z{sub 2} symmetry breaking in the orbifold daughter of N=1 super-Yang-Mills theory, fractional domain walls and vacuum structure. United States. doi:10.1103/PhysRevD.72.105001.
Armoni, A., Gorsky, A., Institute of Theoretical and Experimental Physics, Moscow 117259, and Shifman, M.. Tue . "Spontaneous Z{sub 2} symmetry breaking in the orbifold daughter of N=1 super-Yang-Mills theory, fractional domain walls and vacuum structure". United States. doi:10.1103/PhysRevD.72.105001.
@article{osti_20711580,
title = {Spontaneous Z{sub 2} symmetry breaking in the orbifold daughter of N=1 super-Yang-Mills theory, fractional domain walls and vacuum structure},
author = {Armoni, A. and Gorsky, A. and Institute of Theoretical and Experimental Physics, Moscow 117259 and Shifman, M.},
abstractNote = {We discuss the fate of the Z{sub 2} symmetry and the vacuum structure in a SU(N)xSU(N) gauge theory with one bifundamental Dirac fermion. This theory can be obtained from SU(2N) supersymmetric Yang-Mills theory by virtue of Z{sub 2} orbifolding. We analyze dynamics of domain walls and argue that the Z{sub 2} symmetry is spontaneously broken. Since unbroken Z{sub 2} is a necessary condition for nonperturbative planar equivalence we conclude that the orbifold daughter is nonperturbatively nonequivalent to its supersymmetric parent. En route, our investigation reveals the existence of fractional domain walls, similar to fractional D-branes of string theory on orbifolds. We conjecture on the fate of these domain walls in the true solution of the Z{sub 2}-broken orbifold theory. We also comment on relation with nonsupersymmetric string theories and closed-string tachyon condensation.},
doi = {10.1103/PhysRevD.72.105001},
journal = {Physical Review. D, Particles Fields},
number = 10,
volume = 72,
place = {United States},
year = {Tue Nov 15 00:00:00 EST 2005},
month = {Tue Nov 15 00:00:00 EST 2005}
}
  • We investigate the vacuum structure of pure SU(N) N=1 super Yang-Mills theory. The theory is expected to possess N vacua with associated domain walls. We show that the newly extended version of the low energy effective Lagrangian for super Yang-Mills theory supports the Bogomol'nyi-Prasad-Sommerfield (BPS) domain wall solutions associated with any two vacua aligned with the origin of the moduli space. For the two color theory the domain wall analysis is complete. We also find new non-BPS domain wall solutions connecting any two vacua of the underlying SU(N) super Yang-Mills theory not necessarily aligned. When two vacua are aligned withmore » the origin of the moduli space these solutions are the BPS ones. We also discuss the generic BPS domain wall solutions connecting any two vacua within the extended Veneziano-Yankielowicz theory.« less
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  • An analysis is made of the form of the vacuum condensates and the number of Goldstone bosons in Yang--Mills theories with fermions in the irreducible real representations of the gauge group. A description is given of the physical content of the Yang--Mills supersymmetric theory with N = 2 in the confinement phase.
  • In previous work, we found that necessary and sufficient conditions for large N{sub c} equivalence between parent and daughter theories, for a wide class of orbifold projections of U(N{sub c}) gauge theories, are just the natural requirements that the discrete symmetry used to define the projection not be spontaneously broken in the parent theory, and the discrete symmetry permuting equivalent gauge group factors not be spontaneously broken in the daughter theory. In this paper, we discuss the application of this result to Z{sub k} projections of N=1 supersymmetric Yang-Mills theory in four dimensions, as well as various multiflavor generalizations. Z{submore » k} projections with k>2 yielding chiral gauge theories violate the symmetry realization conditions needed for large N{sub c} equivalence, due to the spontaneous symmetry breaking of discrete chiral symmetry in the parent super-Yang-Mills theory. But for Z{sub 2} projections, we show that previous assertions of large N{sub c} inequivalence, in infinite volume, between the parent and daughter theories were based on incorrect mappings of vacuum energies, theta angles, or connected correlators between the two theories. With the correct identifications, there is no sign of any inconsistency. A subtle but essential feature of the connection between parent and daughter theories involves multivaluedness in the mapping of theta parameters from parent to daughter.« less