Abstract
We present integrable Yang-Baxter deformations of the AdS5 × S5 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 AdS5 × S5.
Highlights
These generalized backgrounds are related to the standard supergravity equations by T -dualizing a supergravity target space in a isometric direction which is a symmetry of all the fields except for the dilaton transforming linearly in this direction [16, 17]
We have shown how to build homogeneous YB deformations for the PS superstring in AdS5 × S5 by exploiting its BRST symmetry and using homological perturbation theory
Even though we restricted our analysis to the case where the R-matrix satisfies the homogeneous CYBE, the extension to the non-homogeneous case should proceed along the same lines as in [40] and we expect a simple relation between them as in the case of deformed GS superstrings [6, 8]
Summary
Recall that the anti-fields were introduced in order to get an off-shell nilpotent BRST charge. The deformed action obtained in the last section (3.25) is non polynomial due to the projectors P which emerged as a consequence of the BRST transformation on the anti-fields (3.11) and (3.12). Taking into account the above results the complete deformed action is given by the local expansion η 4 Str(j+, U(η)Rj−). U(η) = (ηR ◦ Ad−g 1 ◦ dPS ◦ Adg)n We can rearrange this action into a more familiar form by defining the operators. Q(g) = {(1 − ηRg) λ1 + (1 + ηRg) λ3}g , Q(w3−) = −J3− − 4ηP3 ◦ OP−S1−RgN0− , Q(w1+) = −J1+ + 4ηP1 ◦ OP−S1+RgN0+ This can be shown by splitting the action into four sectors. +4ηStr( λ1, [J3−, OP−S1+RgN0+])−4ηStr( λ3, [J0−, OP−S1+RgN0+]) , Str( Q(J0+), N0−) = Str( λ3, [J1+, N0−])−4Str( λ1, ∂+(OP−S1−RgN0−])+. The contributions (4.26), (4.30), (4.33), (4.34), (4.35), (4.37), (4.38), and (4.39) vanish showing that the action is BRST invariant
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