Volume independence in large Nc QCD-like gauge theories
By P. Kovtun, M. Unsal, Laurence G. Yaffe. 2007
179 citations recorded by the source corpus.
Volume independence in large Nc 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 Nc 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 Nc ``orientifold'' equivalence, provided charge conjugation symmetry is unbroken in the latter theory. Therefore, via a combined orbifold-orientifold mapping, a well-defined large Nc 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 Nc QCD in infinite volume.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/155e85b2147ff56016b8cbf49700010546d30774
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In Nuclear and High Energy Physics
Citations in the corpus
- Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles (2014, methodology): “Note that the expressions for the twist free energy is very similar to the effective potential for the eigenvalues of Polyakov loops in SU(N) gauge theories on R3×S1[16, 73] with Nf adjoint Weyl fermions.”
- The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects (2012, background): “This is due to large-N volume independence: at large N an SU(N) gauge theory on R4 is non-perturbatively equivalent to its compactified version on T d × R4−d, where T d is a d-dimensional torus, provided center and translation symmetries are unbroken [1, 8].”
- Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model (2012, methodology): “5) has a non-trivial dependence on the number of flavors, in close analogy with QCD(adj) with Nf Majorana fermions in 4d [80].”