Deformations, renormgroup, symmetries, AdS/CFT

Abstract

We consider the deformations of a supersymmetric quantum field theory by adding spacetime-dependent terms to the action. We propose to describe the renormalization of such deformations in terms of some cohomological invariants, a class of solutions of a Maurer-Cartan equation. We consider the strongly coupled limit of $N=4$ supersymmetric Yang-Mills theory. In the context of AdS/CFT correspondence, we explain what corresponds to our invariants in classical supergravity. There is a leg amputation procedure, which constructs a solution of the Maurer-Cartan equation from tree diagramms of SUGRA. We consider a particular example of the beta-deformation. It is known that the leading term of the beta-function is cubic in the parameter of the beta-deformation. We give a cohomological interpretation of this leading term. We conjecture that it is actually encoded in some simpler cohomology class, which is quadratic in the parameter of the beta-deformation.

arXiv commentv2:small corrections, v3: substantial changes in Section 4(former 6), rewritten Introduction, added Conclusion, references

References in corpus (22)

• Lecture Notes on Holographic Renormalization
• Holographic Renormalization
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• On integrability of the Yang-Baxter $\si$-model
• An integrable deformation of the AdS_5 x S^5 superstring action
• Higher Spin Gauge Theories in Various Dimensions
• Ten-Dimensional Supergravity Constraints from the Pure Spinor Formalism for the Superstring
• An Integrable Deformation of the AdS5 x S5 Superstring
• Deformations of N=4 SYM and integrable spin chain models
• On Exactly Marginal Deformations of N=4 SYM and Type IIB Supergravity on AdS_5 * S^5
• The general Leigh-Strassler deformation and integrability
• Formal Higher-Spin Theories and Kontsevich-Shoikhet-Tsygan Formality
• Notes on beta-deformations of the pure spinor superstring in AdS(5) x S(5)
• Symmetries of massless vertex operators in AdS(5) x S(5)
• Cornering the unphysical vertex
• Finite dimensional vertex
• The Anatomy of Gauge/String Duality in Lunin-Maldacena Background
• Yang-Baxter Deformations of the $Ad{S}_5\times S^5$ Pure Spinor Superstring
• The Algebra of Diffeomorphisms from the World Sheet
• Supermultiplet of $\beta -$deformations from twistors
• On worldsheet curvature coupling in pure spinor sigma-model

Cited by in corpus (1)

• Derived brackets in bosonic string worldsheet sigma-model