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Title: Volume Independence in Large Nc QCD-like Gauge Theories

Abstract

Volume independence in large N{sub c} gauge theories may be viewed as a generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai reduction) is a special case of this equivalence. So is temperature independence in confining phases. A natural generalization concerns volume independence in ''theory space'' of quiver gauge theories. In pure Yang-Mills theory, the failure of volume independence for sufficiently small volumes (at weak coupling) due to spontaneous breaking of center symmetry, together with its validity above a critical size, nicely illustrate the symmetry realization conditions which are both necessary and sufficient for large N{sub c} orbifold equivalence. The existence of a minimal size below which volume independence fails also applies to Yang-Mills theory with antisymmetric representation fermions [QCD(AS)]. However, in Yang-Mills theory with adjoint representation fermions [QCD(Adj)], endowed with periodic boundary conditions, volume independence remains valid down to arbitrarily small size. In sufficiently large volumes, QCD(Adj) and QCD(AS) have a large N{sub c} ''orientifold'' equivalence, provided charge conjugation symmetry is unbroken in the latter theory. Therefore, via a combined orbifold-orientifold mapping, a well-defined large N{sub c} equivalence exists between QCD(AS) in large, or infinite, volume and QCD(Adj) in arbitrarily small volume. Since asymptotically free gauge theories, suchmore » as QCD(Adj), are much easier to study (analytically or numerically) in small volume, this equivalence should allow greater understanding of large N{sub c} QCD in infinite volume.« less

Authors:
; ;
Publication Date:
Research Org.:
Stanford Linear Accelerator Center (SLAC)
Sponsoring Org.:
USDOE
OSTI Identifier:
899207
Report Number(s):
SLAC-PUB-12331
hep-th/0702021; TRN: US0701928
DOE Contract Number:
AC02-76SF00515
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of High Energy Physics (JHEP)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; CRITICAL SIZE; FERMIONS; QUANTUM CHROMODYNAMICS; SYMMETRY; YANG-MILLS THEORY; Theory-HEP,HEPTH

Citation Formats

Kovtun, Pavel, Unsal, Mithat, and Yaffe, Laurence G. Volume Independence in Large Nc QCD-like Gauge Theories. United States: N. p., 2007. Web. doi:10.1088/1126-6708/2007/06/019.
Kovtun, Pavel, Unsal, Mithat, & Yaffe, Laurence G. Volume Independence in Large Nc QCD-like Gauge Theories. United States. doi:10.1088/1126-6708/2007/06/019.
Kovtun, Pavel, Unsal, Mithat, and Yaffe, Laurence G. Tue . "Volume Independence in Large Nc QCD-like Gauge Theories". United States. doi:10.1088/1126-6708/2007/06/019. https://www.osti.gov/servlets/purl/899207.
@article{osti_899207,
title = {Volume Independence in Large Nc QCD-like Gauge Theories},
author = {Kovtun, Pavel and Unsal, Mithat and Yaffe, Laurence G.},
abstractNote = {Volume independence in large N{sub c} gauge theories may be viewed as a generalized orbifold equivalence. The reduction to zero volume (or Eguchi-Kawai reduction) is a special case of this equivalence. So is temperature independence in confining phases. A natural generalization concerns volume independence in ''theory space'' of quiver gauge theories. In pure Yang-Mills theory, the failure of volume independence for sufficiently small volumes (at weak coupling) due to spontaneous breaking of center symmetry, together with its validity above a critical size, nicely illustrate the symmetry realization conditions which are both necessary and sufficient for large N{sub c} orbifold equivalence. The existence of a minimal size below which volume independence fails also applies to Yang-Mills theory with antisymmetric representation fermions [QCD(AS)]. However, in Yang-Mills theory with adjoint representation fermions [QCD(Adj)], endowed with periodic boundary conditions, volume independence remains valid down to arbitrarily small size. In sufficiently large volumes, QCD(Adj) and QCD(AS) have a large N{sub c} ''orientifold'' equivalence, provided charge conjugation symmetry is unbroken in the latter theory. Therefore, via a combined orbifold-orientifold mapping, a well-defined large N{sub c} equivalence exists between QCD(AS) in large, or infinite, volume and QCD(Adj) in arbitrarily small volume. Since asymptotically free gauge theories, such as QCD(Adj), are much easier to study (analytically or numerically) in small volume, this equivalence should allow greater understanding of large N{sub c} QCD in infinite volume.},
doi = {10.1088/1126-6708/2007/06/019},
journal = {Journal of High Energy Physics (JHEP)},
number = ,
volume = ,
place = {United States},
year = {Tue Feb 06 00:00:00 EST 2007},
month = {Tue Feb 06 00:00:00 EST 2007}
}
  • Consequences of large N volume independence are examined in conformal and confining gauge theories. In the large N limit, gauge theories compactified on R{sup d-k} x (S{sup 1}){sup k} are independent of the S{sup 1} radii, provided the theory has unbroken center symmetry. In particular, this implies that a large N gauge theory which, on R{sup d}, flows to an IR fixed point, retains the infinite correlation length and other scale invariant properties of the decompactified theory even when compactified on R{sup d-k} x (S{sup 1}){sup k}. In other words, finite volume effects are 1/N suppressed. In lattice formulations ofmore » vector-like theories, this implies that numerical studies to determine the boundary between confined and conformal phases may be performed on one-site lattice models. In N = 4 supersymmetric Yang-Mills theory, the center symmetry realization is a matter of choice: the theory on R{sup 4-k} x (S{sup 1}){sup k} has a moduli space which contains points with all possible realizations of center symmetry. Large N QCD with massive adjoint fermions and one or two compactified dimensions has a rich phase structure with an infinite number of phase transitions coalescing in the zero radius limit.« less
  • This paper investigates the phase structure of (QCD-like) gauged Nambu-Jona-Lasinio model (QCD-like gauge theories plus four-fermion interactions) based on the ladder Schwinger-Dyson equation with one-loop running gauge coupling. Through analytical and numerical studies, the authors establish two fixed points structure, one with a large anomalous dimension {gamma}{sub m} {approx equal} 2 and the other with a small one {gamma}{sub m} {approx equal} 0. The authors further obtain the power critical exponents through the equation of state, which, as they stand, imply that the former fixed point is a Gaussian fixed point. The authors emphasize that logarithmic corrections due to themore » gauge interaction is crucial to obtaining an interacting continuum theory at this fixed point.« less
  • We consider QCD-like theories with one massless fermion in various representations of the gauge group SU(N). The theories are formulated on R{sub 3} x S{sub 1}. In the decompactification limit of large r(S{sub 1}) all these theories are characterized by confinement, mass gap and spontaneous breaking of a (discrete) chiral symmetry ({chi}SB). At small r(S{sub 1}), in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double trace deformation. With these deformation, the theories at hand are at weak coupling at small r(S{sub 1}) and yet exhibit basic features of the large-r(S{submore » 1}) limit: confinement and {chi}SB. We calculate the string tension, mass gap, bifermion condensates and {theta} dependence. The double-trace deformation becomes dynamically irrelevant at large r(S{sub 1}). Despite the fact that at small r(S{sub 1}) confinement is Abelian, while it is expected to be non-Abelian at large r(S{sub 1}), we argue that small and large-r(S{sub 1}) physics are continuously connected. If so, one can use small-r(S{sub 1}) laboratory to extract lessons about QCD and QCD-like theories on R{sub 4}.« less
  • Large-N QCD with heavy adjoint fermions emulates pure Yang-Mills theory at long distances. We study this theory on a four- and three-torus, and analytically argue the existence of a large-small volume equivalence. For any finite mass, center symmetry unbroken phase exists at sufficiently small volume and this phase can be used to study the large-volume limit through the Eguchi-Kawai equivalence. A finite temperature version of volume independence implies that thermodynamics on R3 x S1 can be studied via a unitary matrix quantum mechanics on S1, by varying the temperature. To confirm this non-perturbatively, we numerically study both zero- and one-dimensionalmore » theories by using Monte-Carlo simulation. Order of finite-N corrections turns out to be 1/N. We introduce various twisted versions of the reduced QCD which systematically suppress finite-N corrections. Using a twisted model, we observe the confinement/deconfinement transition on a 1{sup 3} x 2-lattice. The result agrees with large volume simulations of Yang-Mills theory. We also comment that the twisted model can serve as a non-perturbative formulation of the non-commutative Yang-Mills theory.« less
  • We consider QCD-like theories with one massless fermion in various representations of the gauge group SU(N). The theories are formulated on R{sub 3}xS{sub 1}. In the decompactification limit of large r(S{sub 1}) all these theories are characterized by confinement, mass gap, and spontaneous breaking of a (discrete) chiral symmetry ({chi}SB). At small r(S{sub 1}), in order to stabilize the vacua of these theories at a center-symmetric point, we suggest to perform a double-trace deformation. With this deformation, the theories at hand are at weak coupling at small r(S{sub 1}) and yet exhibit basic features of the large r(S{sub 1}) limit:more » confinement and {chi}SB. We calculate the string tension, mass gap, bifermion condensates, and {theta} dependence. The double-trace deformation becomes dynamically irrelevant at large r(S{sub 1}). Despite the fact that at small r(S{sub 1}) confinement is Abelian, while it is expected to be non-Abelian at large r(S{sub 1}), we argue that small and large r(S{sub 1}) physics are continuously connected. If so, one can use small r(S{sub 1}) laboratory to extract lessons about QCD and QCD-like theories on R{sub 4}.« less