Exact probes of orientifolds

Abstract

We compute the exact vacuum expectation value of circular Wilson loops for Euclidean N = 4 super Yang-Mills with G = SO(N ), Sp(N ), in the fundamental and spinor representations. These field theories are dual to type IIB string theory compactified on AdS 5 × RP 5 plus certain choices of discrete torsion, and we use our results to probe this holographic duality. We first revisit the LLM-type geometries having AdS 5 × RP 5 as ground state. Our results clarify and refine the identification of these LLM-type geometries as bubbling geometries arising from fermions on a half harmonic oscillator. We furthermore identify the presence of discrete torsion with the one-fermion Wigner distribution becoming negative at the origin of phase space. We then turn to the string world-sheet interpretation of our results and argue that for the quantities considered they imply two features: first, the contribution coming from world-sheets with a single crosscap is closely related to the contribution coming from orientable world-sheets, and second, world-sheets with two crosscaps don't contribute to these quantities.

Probing N = 2 $$ \mathcal{N}=2 $$ superconformal field theories with localization

“…These results are to be contrasted with the well-known corresponding results for N = 4 SYM. In this case, all these coefficients are essentially the same due to the extra amount of supersymmetry, B = 3h W = 4f W , and can be computed exactly [10,13] for various gauge groups and representations [14,15]. In the large N, large λ regime, they scale as √ λ.…”

Cusped Wilson lines in symmetric representations

“…Circular Wilson loops and cusp anomalous dimensions for these groups have recently been studied in[39].…”

Wilson loops in terms of color invariants

“…[21] -and valid for any G and any R. It encompasses and unifies all the known results for particular choices of G and R[25][26][27]. Now it is a matter of evaluating d a 1 a 1 ...a k a k…”

“…found in [27]. Moreover, (2.7) implies that the vevs of Wilson loops in the symmetric and antisymmetric representations of SU(N ) satisfy…”

“…In this section we revisit the evaluation of W R for N = 4 super Yang Mills, for an arbitrary representation R of a generic Lie algebra G. Thanks to supersymmetric localization [21] this problem reduces to a Gaussian matrix model, and it has been solved exactly, for various choices of gauge group G and representation R [25][26][27].…”