A note on the dual of N=1 super-Yang–Mills theory

Abstract

We refine the dictionary of the gauge/gravity correspondence realizing N = 1 super Yang-Mills by means of D5-branes wrapped on a resolved Calabi-Yau space. This is done by fixing an ambiguity on the correct interpretation of the holographic dual of the running gauge coupling and amounts to identify a specific 2-cycle in the dual ten-dimensional supergravity background. In doing so, we also discuss the role played in this context by gauge transformations in the relevant seven-dimensional gauged supergravity. While all nice properties of the duality are maintained, this modification of the dictionary has some interesting physical consequences and solves a puzzle recently raised in the literature. In this refined framework, it is also straightforward to see how the correspondence naturally realizes a geometric transition.

Perturbative and non-perturbative aspects of pure Script N = 1 super Yang-Mills theory from wrapped branes

“…Thus, we obtain the correct (and in general non-vanishing) θ YM . In contrast, the wrapping of [11] yields a θ YM differing from our result by a factor 1/2 (with a somewhat difficult interpretation of the chiral symmetry), while the result of [21] corresponds to the special case θ YM = 0. Sec.…”

“…In the regular case, c = 0, the gauge coupling, g YM , diverges at ρ = 0, signalling the disappearance of the UV degrees of freedom at the vacuum. This exact RG flow was analyzed in [21] for the special case ψ = ψ 0 .…”

“…The main result will be the calculation of the beta function. In contrast to [21] we shall average the probe gauge coupling over all inequivalent vacua in order to confront its running with a perturbative field theory analysis. This will not only remove a spurious energy dependence from θ YM , but we will also be able to exactly re-write the beta function in terms of gauge theory quantities.…”

Semi-classical string solutions for =1 SYM

“…By virtue of (3.13), and bearing in mind that we have just argued that (3.12) holds at any g s , this implies N → ∞. The value of λ t ′ Hooft = g 2 YM N can be read directly from the behaviour of the β-function [28,29] 1…”

“…To be more definite, even if the prefactor e 2g(ρ) of the S 2 vanishes in this limit, the contribution of the a(ρ) field remains -due to the twisting-preventing the S 2 from eventually shrinking. Probably this can be amended by using the S 2 parametrisation of [29].…”