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Non-Perturbative Planar Equivalence and the Absence of Closed String Tachyons
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Preprint typeset in JHEP style - HYPER VERSION
Non-Perturbative Planar Equivalence and the
Absence of Closed String Tachyons
Adi Armoni
Department of Physics,
Swansea University,
Swansea, SA2 8PP, UK.
E-mail: a.armoni@swan.ac.uk
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 R3 × S1. In the specific case of U(N)
theories with symmetric/anti-symmetric fermions (’orientifold field theories’) the rel-
evant 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 find-
ing 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 ra-
dius increases. In the case of U(N) × U(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 ’ori-
entfiold 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.
Keywords: AdS/CFT, large N , Branes.
1. Introduction
Planar equivalence between supersymmetric and non-supersymmetric gauge theories
[1,2] proved itself as a useful tool in the study of non-perturbative QCD (see [3,4] for
reviews). Besides its important application for QCD, it is an interesting statement in
field-theory per-se: a susy/n
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