Holographic calculations of Euclidean Wilson loop correlator in Euclidean anti-de Sitter space
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The correlation functions of two or more Euclidean Wilson loops of various shapes in Euclidean anti-de Sitter space are computed by considering the minimal area surfaces connecting the loops. The surfaces are parametrized by Riemann theta functions associated with genus three hyperelliptic Riemann surfaces. In the case of two loops, the distance L by which they are separated can be adjusted by continuously varying a specific branch point of the auxiliary Riemann surface. When L is much larger than the characteristic size of the loops, then the loops are approximately regarded as local operators and their correlator as the correlator of two local operators. Similarly, when a loop is very small compared to the size of another loop, the small loop is considered as a local operator corresponding to a light supergravity mode.
KeywordsAdS-CFT Correspondence Long strings
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- E.D. Belokolos, A.I. Bobenko, V.Z. Enol’skii, A.R. Its and V.B. Matveev, Algebro-Geometric Approach to Nonlinear Integrable Equations, Springer-Verlag series in Non-linear Dynamics, Springer-Verlag, Heidelberg Germany (1994).Google Scholar
- R. Miranda, Graduate Studies in Mathematics. Vol. 5: Algebraic Curves and Riemann Surfaces, AMS Press, Providence Germany (1995).Google Scholar
- C. Birkenhake and H. Lange, Grundlehren der mathematischen Wissenschaften. Vol. 302: Complex Abelian Varieties, Springer-Verlag, Heidelberg Germany (2004).Google Scholar
- H.M. Farkas and I. Kra, Graduate Texts in Mathematics. Vol. 71: Riemann Surfaces, second edition, Springer-Verlag, Heidelberg Germany (1991).Google Scholar
- A.I. Bobenko and C. Klein, Lecture Notes in Mathematics. Vol. 2013: Computational Approach to Riemann Surfaces, Springer-Verlag, Berlin Germany (2011).Google Scholar