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Journal of High Energy Physics

, 2014:169

First Online: 29 September 2014Received: 09 July 2014Accepted: 07 September 2014 Abstract

We compute the exact vacuum expectation value of circular Wilson loops for Euclidean \ \mathcal{N} \ = 4 super Yang-Mills with G = SON,SpN, in the fundamental and spinor representations. These field theories are dual to type IIB string theory compactified on AdS5 × \ \mathbb{R}{\mathrm{\mathbb{P}}}^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 AdS5 × \ \mathbb{R}{\mathrm{\mathbb{P}}}^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.

KeywordsWilson ’t Hooft and Polyakov loops 1-N Expansion AdS-CFT Correspondence ArXiv ePrint: 1406.5129

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Author: Bartomeu Fiol - Blai Garolera - Genís Torrents

Source: https://link.springer.com/

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