A minimalistic pure spinor sigma-model in AdS

At small AdS radius, the superstring on AdS 5 × S 5 was conjectured by Maldacena to be equivalent to N = 4 super-Yang-Mills at small 't Hooft coupling where thickened Feynman diagrams can be used to compute scattering amplitudes. It was previously shown that the pure spinor worldsheet action of the AdS 5 × S 5 superstring can be expressed as the sum of a BRST-trivial term and a "B-term" which is antisymmetric in worldsheet derivatives. Using the explicit form of the pure spinor vertex operators, it will be argued here that the free super-Yang-Mills Feynman diagrams are described by the BRST-trivial term where the thickened propagators are the regions of the string worldsheet near the AdS boundary and the holes are the regions near the AdS horizon. Evidence will then be presented that the antisymmetric B-term generates the super-Yang-Mills vertex so that, at small radius and arbitrary genus, the superstring amplitudes correctly reproduce the super-Yang-Mills Feynman diagram expansion.

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Sketching a proof of the Maldacena conjecture at small radius

Berkovits

2019

“…At this time, we do not have concrete examples of string worldsheet theories where Dg would not enter only through the projection to Cg. It is likely that pure spinor superstring in AdS background is an example, but we only have a partial construction [6]. JHEP12(2020)077…”

Section: Vertex Operatorsmentioning

confidence: 99%

DGLA Dg and BV formalism

Mikhailov

2020

Self Cite

Differrential Graded Lie Algebra Dg was previously introduced in the context of current algebras. We show that under some conditions, the problem of constructing equivariantly closed form from closed invariant form is reduces to construction of a representation of Dg. This includes equivariant BV formalism. In particular, an analogue of intertwiner between Weil and Cartan models allows to clarify the general relation between integrated and unintegrated operators in string worldsheet theory.

“…An analogous result is obtained for ω * 3− . Thus, the BRST charge Q = Q 0 + ηQ 1 is nilpotent if R is a solution of the CYBE [49].…”

Section: Jhep02(2019)056mentioning

confidence: 99%

Yang-Baxter deformations of the AdS5 × S5 pure spinor superstring

Benítez

Rivelles

2019

We present integrable Yang-Baxter deformations of the AdS 5 × S 5 pure spinor superstring theory which were obtained by using homological perturbation theory. Its equations of motion and BRST symmetry are discussed and its Lax connection is derived. We also show that its target space background is the same generalized supergravity background found for Yang-Baxter deformations of the Green-Schwarz superstring in AdS 5 × S 5 .