From effective actions to the background geometry

Abstract

We discuss how the background geometry can be traced from the one-loop effective actions in nonsupersymmetric theories in the external abelian fields. It is shown that upon the proper identification of the Schwinger parameter the Heisenberg-Euler abelian effective action involves the integration over the $Ad{S}_3$, $S_3$ and $T^{\ast }{S}^3$ geometries, depending on the type of the external field. The interpretation of the effective action in the sefdual field in terms of the topological strings is found and the corresponding matrix model description is suggested. It is shown that the low energy abelian MHV one-loop amplitudes are expressed in terms of the type B topological string amplitudes in mirror to $T^{\ast }{S}^3$ manifold. We also make some comments on the relation between the imaginary part of the effective action and the branes in SU(2) as well as on the geometry of the contours relevant for the path integral.

Latex. 40 pages, typos corrected, references added

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• From Free Fields to $AdS$ -- III
• Brane Partons and Singleton Strings
• From Yang-Mills Lagrangian to MHV Diagrams
• Chern-Simons matrix models and Stieltjes-Wigert polynomials
• Discrete and oscillatory Matrix Models in Chern-Simons theory
• Aspects of the N=4 SYM amplitude -- Wilson polygon duality
• The Condensate from Torus Knots
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
• One-loop derivation of the Wilson polygon - MHV amplitude duality
• Angular Momentum and Gravimagnetization of the $\mathcal{N}=2$ SYM vacuum
• Metal or Insulator? Dirac operator spectrum in holographic QCD
• Instanton-torus knot duality in 5d SQED and $SU(2)$ SQCD