Non-critical superstrings from four-dimensional gauge theory

Abstract

We study large-N double-scaling limits of U(N) gauge theories in four dimensions. We focus on theories in a partially confining phase where an abelian subgroupĜ of the gauge group remains unconfined. Double-scaling is defined near critical points in the parameter/moduli space where states charged underĜ become massless. In specific cases, we present evidence that the double-scaled theory is dual to a non-critical superstring background. Models studied include the β-deformation of N = 4 SUSY Yang-Mills which leads to a non-critical string theory with sixteen supercharges. We also study N = 1 SUSY Yang-Mills theory coupled to a single chiral superfield with a polynomial superpotential which leads to a related string theory with eight supercharges. In both cases the string coupling is small and the background is free from Ramond-Ramond flux.

Double scaling limits in gauge theories and matrix models

“…In particular, the effects of the glueball superpotential do not vanish in the limit. Thus, even though the field theory analysis clearly shows that the double-scaling limit still selects a particular sector of the theory which has non-trivial dynamics, we do not identify the would-be non-critical string dual as in [4]. For the type of singularities studied in the old matrix model to describe twodimensional gravity coupled to c < 1 conformal field theories, where the near-critical curve has only one branch point along with any arbitrary number of double points, the double-scaling limit describes a sector of a gauge theory with a mass gap and light meson-like composite states which we argued are the approximate Goldstone bosons of superconformal invariance.…”

“…Even though we do not have control over the kinetic terms of the glueball states, we take this behaviour of the Hessian matrix to signal that, with double points, the masses of the glueball fields become very large in the double-scaling limit. This is to be contrasted with the case without double points studied in [4], where the appearance of the [n/2] massless glueballs was interpreted as evidence that supersymmetry is enhanced to N = 2 in the doublescaling limit.…”

“…In [43], the methods of [40,41,64] are used to evaluate the genus one and two terms of the matrix model free energy for the class of double-scaling limits considered in [4]. The simplest case corresponds to the above conifold singularity with two branch points colliding and no double points, n = 2, m = 0, and the results match the genus zero, one and two terms in (4.12).…”

“…This is the situation considered in [4,31,32]. In this case, we first consider the consistency conditions (2.14) for a U(p = n) gauge theory with W (x) of order ℓ = n + 1.…”

“…Note that the g = 0 term of Γ 1 is the ordinary glueball superpotential: 9) which determines the vacua of the theory. 4 In the usual large-N limit, the contribution from a genus g graph is suppressed by N 2−2g . However, if there is a scenario as described above where a state is becoming massless then this suppression can be subverted.…”