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Polyvector deformations of Type IIB backgrounds

Kirill Gubarev, Edvard T. Musaev, Timophey Petrov

TL;DR

This work develops a formalism for polyvector deformations of Type IIB backgrounds within the $\mathrm{E}_{6(6)}$ exceptional field theory, focusing on 4-vector deformations parameterized by a 4-vector $\Omega^{mnkl}$ and a bi-vector doublet $\beta_{\alpha}^{mn}$. By embedding Type IIB into ExFT and truncating to a $D=5$ gauged-like sector, the authors derive explicit transformation rules for the internal generalized metric and map these to Type IIB fields, obtaining a concrete deformation recipe. They show that invariance of the generalized fluxes $\mathcal{F}_{AB}{}^{C}$ yields quadratic algebraic conditions—generalized Yang–Baxter equations and unimodularity—that guarantee the deformed background solves the Type IIB equations; these conditions reproduce the Type IIB Exceptional Drinfeld algebra constraints. An explicit AdS$_5\times$S$^5$ example (a DPPP-type 4-vector deformation) demonstrates the method: the deformed metric and self-dual 5-form flux are given, with a null condition $\rho^2=0$ ensuring a solution, illustrating how new exactly marginal or non-supersymmetric deformations arise. Overall, the paper extends the solution-generating toolkit for Type IIB supergravity using ExFT and links polyvector deformations to EDA structures, offering avenues to uncover novel holographic duals.

Abstract

We develop a formalism of poly-vector deformations for Type IIB backgrounds with a block diagonal metric and non-vanishing self-dual 5-form RR field strength. Making use of the embedding of the Type IIB theory into the $\mathrm{E}_{6(6)}$ exceptional field theory we derive explicit transformation rules for four-vector deformations. We prove that the algebraic condition following from the Type IIB realization of exceptional Drinfeld algebras is sufficient for the transformation to generate a solution.

Polyvector deformations of Type IIB backgrounds

TL;DR

This work develops a formalism for polyvector deformations of Type IIB backgrounds within the exceptional field theory, focusing on 4-vector deformations parameterized by a 4-vector and a bi-vector doublet . By embedding Type IIB into ExFT and truncating to a gauged-like sector, the authors derive explicit transformation rules for the internal generalized metric and map these to Type IIB fields, obtaining a concrete deformation recipe. They show that invariance of the generalized fluxes yields quadratic algebraic conditions—generalized Yang–Baxter equations and unimodularity—that guarantee the deformed background solves the Type IIB equations; these conditions reproduce the Type IIB Exceptional Drinfeld algebra constraints. An explicit AdSS example (a DPPP-type 4-vector deformation) demonstrates the method: the deformed metric and self-dual 5-form flux are given, with a null condition ensuring a solution, illustrating how new exactly marginal or non-supersymmetric deformations arise. Overall, the paper extends the solution-generating toolkit for Type IIB supergravity using ExFT and links polyvector deformations to EDA structures, offering avenues to uncover novel holographic duals.

Abstract

We develop a formalism of poly-vector deformations for Type IIB backgrounds with a block diagonal metric and non-vanishing self-dual 5-form RR field strength. Making use of the embedding of the Type IIB theory into the exceptional field theory we derive explicit transformation rules for four-vector deformations. We prove that the algebraic condition following from the Type IIB realization of exceptional Drinfeld algebras is sufficient for the transformation to generate a solution.
Paper Structure (15 sections, 79 equations, 1 figure)

This paper contains 15 sections, 79 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Embedding of Type IIB into the E6 ExFT
  3. Field content and geometric embedding
  4. Truncated ExFT in IIB parametrization
  5. Generators and the generalized metric
  6. Type IIB fields
  7. Deformations in the truncated Type IIB theory
  8. 4-vector transformation rules
  9. Transformation of fluxes
  10. Type IIB Exceptional Drinfeld algebra
  11. Example of 4-vector deformation of AdS5xS5
  12. Conclusions
  13. Index conventions
  14. E6 algebra in the Type IIB decomposition
  15. Transformation of the generalized fluxes

Figures (1)

  • Figure 1: Representation of the embedding of Type IIB into the $\mathrm{E}_{6(6)}$ ExFT. First layer of arrows (red) denotes the $10=5+5$ split of coordinates according to the standard KK ansatz. The bottom layer of arrows schematically shows how the result is combined into the fields of ExFT. The rounded rectangle combines fields that are dual. The 4-form $C_{\mu\nu\rho\sigma}$ is non-dynamical and its field strength contributes to the embedding tensor of gauged supergravity.