D-brane charges in gravitational duals of 2 + 1 dimensional gauge theories and duality cascades

Abstract

We perform a systematic analysis of the D-brane charges associated with string theory realizations of d = 3 gauge theories, focusing on the examples of the N = 4 supersymmetric U (N ) × U (N + M ) Yang-Mills theory and the N = 3 supersymmetric U (N ) × U (N + M ) Yang-Mills-Chern-Simons theory. We use both the brane construction of these theories and their dual string theory backgrounds in the supergravity approximation. In the N = 4 case we generalize the previously known gravitational duals to arbitrary values of the gauge couplings, and present a precise mapping between the gravity and field theory parameters. In the N = 3 case, which (for some values of N and M ) flows to an N = 6 supersymmetric Chern-Simons-matter theory in the IR, we argue that the careful analysis of the charges leads to a shift in the value of the B 2 field in the IR solution by 1/2, in units where its periodicity is one, compared to previous claims. We also suggest that the N = 3 theories may exhibit, for some values of N and M , duality cascades similar to those of the Klebanov-Strassler theory.1 The minus sign is the result of the conventions used in this paper, summarized in appendix B.

Airy function and 4d quantum gravity

“…Although they may yield additional factors of N 2 / √ λ, they are secondary to our main point and may well be cancelled in supersymmetric cases. 5 (4) The shift by −1/(24λ) − λ/(3N 2 ) in the Airy function of ABJM theory (1.1) cannot be accounted for in our approximations, since they originate from higher curvature corrections [30,31].…”

ABJ theory in the higher spin limit

“…The gravity theory is M-theory on AdS 4 × S 7 /Z k with the 3-form field turned on, C 3 ∝ M , and the dual field theory is the N = 6 U(N ) k × U(N + M ) −k Chern-Simons-matter (CSM) theory, called the ABJ theory, where k and −k are the ChernSimons levels for the two gauge groups. At large k, the M-theory circle of radius R 11 = 1/k shrinks and M-theory reduces to type IIA string theory on AdS 4 × CP 3 with the NSNS 2-form turned on, B 2 ∝ M k − 1 2 [55,57,58]. The ingredient crucial to the HS/VM duality is the presence of the B 2 that, in particular, provides U(M ) vectors in the dual field theory.…”

Metastable vacua and the backreacted Stenzel geometry

“…In order to identify the backreacted solution, we need to impose the correct boundary conditions associated to the presence of the anti-branes at the tip. In this section we start by discussing the standard notions of charge in the Stenzel background (see for example [20][21][22]) and as a warmup we identify the BPS perturbation of the CGLP solution ascribed to the presence of M2 branes. The anti-M2 brane perturbation will be discussed in the next section.…”