The Veneziano Limit of N=2 Superconformal QCD: Towards the String Dual of N=2 SU(N_c) SYM with N_f =2 N_c

TL;DR

The paper tackles the AdS dual of ${ m N}=2$ SCQCD in the Veneziano limit, arguing that the flavor-singlet sector is governed by a purely closed-string description and developing a two-pronged program (protected-spectrum analysis in the field theory and brane-based non-critical-string constructions). It identifies an interpolating ${ m N}=2$ theory that connects the ${ m Z}_2$ orbifold of ${ m N}=4$ SYM to ${ m N}=2$ SCQCD and uses the superconformal index to uncover a large, exponentially growing set of extra protected states not visible in a naive truncation. The dual picture emerges as a sub-critical background with an ${ m AdS}_5 imes { m S}^1$ factor, where a sector of light string states persists at all couplings and prevents a purely supergravity description; a seven-dimensional ${ m SO}(4)$-gauged supergravity provides a qualitative effective theory for the low-lying spectrum. Overall, the work provides a coherent framework suggesting that ${ m N}=2$ SCQCD in the Veneziano limit is holographically dual to a non-critical string background, with implications for higher-spin protection and the role of fundamental flavors in holography.

Abstract

We attack the long-standing problem of finding the AdS dual of N = 2 superconformal QCD, the N=2 super Yang Mills theory with gauge group SU(N_c) and N_f = 2 N_c fundamental hyper multiplets. The theory admits a Veneziano expansion of large N_c and large N_f, with N_f/N_c and lambda = g^2 N_c kept fixed. The topological structure of large N diagrams motivates a general conjecture: the flavor-singlet sector of a gauge theory in the Veneziano limit is dual to a closed string theory; single closed string states correspond to "generalized single-trace" operators, where adjoint letters and flavor-contracted fundamental/antifundamental pairs are stringed together in a closed chain. We look for the string dual of N = 2 superconformal QCD from two fronts. From the bottom-up, we perform a systematic analysis of the protected spectrum using superconformal representation theory. We also evaluate the one-loop dilation operator in the scalar sector, finding a novel spin chain. From the top-down, we consider the decoupling limit of known brane constructions. In both approaches, more insight is gained by viewing the theory as the degenerate limit of the N = 2 Z_2 orbifold of N = 4 SYM, as one of the two gauge couplings is tuned to zero. A consistent picture emerges. We conclude that the string dual is a sub-critical background with seven "geometric" dimensions, containing both an AdS_5 and an S^1 factor. The supergravity approximation is never entirely valid, even for large lambda, indeed the field theory has an exponential degeneracy of exactly protected states with higher spin, which must be dual to a sector of light string states.

Figures (4)

• Figure 1: Double line propagators. The adjoint propagator $\langle \phi^{a}_{\; b} \; \phi^{c}_{\; d} \rangle$ on the left, represented by two color lines, and the fundamental propagator $\langle q^{a}_{\; i} \; \bar{q} ^{j}_{\; b} \rangle$ on the right, represented by a color and a flavor line.
• Figure 2: The equivalence classes $[1,1,0]^{\mathtt{L}}_{\pm}$. The multiplets belonging to $[1,1,0]^{\mathtt{L}}_{\pm}$ have index $\pm \mathcal{I}^{\mathtt{L}}_{[1,1,0]}$. The sum of the indices of adjacent multiplets is zero, as required by the recombination rule.
• Figure 3: Example of two configurations of the $\hat{\mathcal{C}}$ multiplets with $R+j+\bar{j}=1$ contributing the same to both $\mathcal{I}^{\mathtt{L}}$ and $\mathcal{I}^{\mathtt{R}}$. The multiplets are denoted by crosses on the $(j , \bar{j})$ grid. The indices are the same for (a) and (b) because the projections on the $j$ and $\bar{j}$ ( i.e. the sets of $j$ and ${\bar{j}}$ values) are the same.
• Figure 4: Hanany-Witten setup for the interpolating SCFT (on the left) and for $\mathcal{N} =2$ SCQCD (on the right).