Non-Perturbative Planar Equivalence and the Absence of Closed String Tachyons

TL;DR

This paper investigates the conditions under which planar equivalence holds in non-supersymmetric gauge theories by analyzing the presence or absence of tachyons in their dual string theories, revealing phase transitions and stability criteria.

Contribution

It establishes a link between the absence of closed string tachyons and the validity of planar equivalence in various gauge theories, providing new insights into their phase structure and dual string descriptions.

Findings

Orientifold theories are tachyon-free at large radius, but develop tachyons below a critical radius.

Orbifold theories always have tachyons, indicating planar equivalence fails.

Planar equivalence holds for SO/Sp gauge theories with symmetric/antisymmetric fermions, consistent with tachyon absence.

Abstract

We consider 'orbifold' and 'orientifold' field theories from the dual closed string theory side. We argue that a necessary condition for planar equivalence to hold is the absence of a closed string tachyonic mode in the dual non-supersymmetric string. We analyze several gauge theories on R3xS1. In the specific case of U(N) theories with symmetric/anti-symmetric fermions ('orientifold field theories') the relevant closed string theory is tachyon-free at large compactification radius (due to winding modes), but it develops a tachyonic mode below a critical radius. Our finding is with agreement with field theory expectations of a phase transition from a C-parity violating phase to a C-parity preserving phase as the compactification radius increases. In the case of U(N)xU(N) theories with bi-fundamental matter ('orbifold field theories') a tachyon is always present in the string spectrum, at any compactification radius. We conclude that on R4 planar equivalence holds for 'orientfiold field theories', but fails for 'orbifold field theories' daughters of N=4 SYM and suggest the same for daughters of N=1 SYM. We also discuss examples of SO/Sp gauge theories with symmetric/anti-symmetric fermions. In this case planar equivalence holds at any compactification radius -in agreement with the absence of tachyons in the string dual.