Quantum corrections to minimal surfaces with mixed three-form flux

Abstract

We obtain the ratio of semiclassical partition functions for the extension under mixed flux of the minimal surfaces subtending a circumference and a line in Euclidean $Ad{S}_3\times S^3\times T^4$. We reduce the problem to the computation of a set of functional determinants. If the Ramond-Ramond flux does not vanish, we find that the contribution of the $B$-field is comprised in the conformal anomaly. In this case, we successively apply the Gel'fand-Yaglom method and the Abel-Plana formula to the flat-measure determinants. To cancel the resultant infrared divergences, we shift the regularization of the sum over half-integers depending on whether it corresponds to massive or massless fermionic modes. We show that the result is compatible with the zeta-function regularization approach. In the limit of pure Neveu-Schwarz-Neveu-Schwarz flux we argue that the computation trivializes. We extend the reasoning to other surfaces with the same behavior in this regime.

arXiv comment32 pages. Latex. v2: Published version, acknowledgement added

References in corpus (36)

• Wilson loops in large N field theories
• Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de Sitter supergravity
• Spinning strings in AdS_5 x S^5 and integrable systems
• Spinning strings in AdS_5 x S^5: new integrable system relations
• Green-Schwarz String in AdS_5 x S^5: Semiclassical Partition Function
• Generalized quark-antiquark potential at weak and strong coupling
• On one-loop correction to energy of spinning strings in S^5
• Matching the circular Wilson loop with dual open string solution at 1-loop in strong coupling
• Functional Determinants in Quantum Field Theory
• On the integrability of Wilson loops in AdS_5 x S^5: Some periodic ansatze
• The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling
• Non-supersymmetric Wilson loop in N=4 SYM and defect 1d CFT
• One-loop Effective Action of the Holographic Antisymmetric Wilson Loop
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• What does the string/gauge correspondence teach us about Wilson loops?
• Quark-antiquark potential in AdS at one loop
• Precision calculation of 1/4-BPS Wilson loops in AdS${}_5\times S^5$
• Perturbative computation of string one-loop corrections to Wilson loop minimal surfaces in $Ad{S}_5\times S^5$
• More about One-Loop Effective Action of Open Superstring in $Ad{S}_5\times S^5$
• Spinning strings and minimal surfaces in $Ad{S}_3$ with mixed 3-form fluxes
• The Subleading Term of the Strong Coupling Expansion of the Heavy-Quark Potential in a $\mathcal{N}=4$ Super Yang-Mills Vacuum
• Toward precision holography with supersymmetric Wilson loops
• Correlation Function of Circular Wilson Loops at Strong Coupling
• The Subleading Term of the Strong Coupling Expansion of the Heavy-Quark Potential in a $\mathcal{N}=4$ Super Yang-Mills Plasma
• String corrections to circular Wilson loop and anomalies
• Precision matching of circular Wilson loops and strings in AdS(5)xS(5)
• One-loop corrections to holographic Wilson loop in AdS4xCP3
• The finite 't Hooft coupling correction on the jet quenching parameter in a $\mathcal{N}=4$ Super Yang-Mills Plasma
• Zeta-function Regularization of Holographic Wilson Loops
• One-loop Holography with Strings in $Ad{S}_4\times {\mathbb{CP}}^3$
• Quantum String Test of Nonconformal Holography
• Toward Precision Holography in Type IIA with Wilson Loops
• Matching quantum string corrections and circular Wilson loops in $Ad{S}_4\times C{P}^3$
• The Partition Function of a Wilson Loop in a Strongly Coupled $\mathcal{N}=4$ Supersymmetric Yang-Mills Plasma with Fluctuations
• Functional Determinants of Radial Operators in $Ad{S}_2$
• Minimal surfaces with mixed three-form flux

Cited by in corpus (3)

• Semiclassical $p$-branes in hyperbolic space
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