TY - JOUR

T1 - Scale invariance of the η-deformed AdS5×S5 superstring, T-duality and modified type II equations

AU - Arutyunov, G.

AU - Frolov, S.

AU - Hoare, B.

AU - Roiban, R.

AU - Tseytlin, A. A.

N1 - Funding Information:
We thank R. Borsato, O. Lunin, S.J. van Tongeren and L. Wulff for useful discussions and O. Lunin and L. Wulff for comments on the draft. The work of G.A. is supported by the German Science Foundation ( DFG ) under the Collaborative Research Center (SFB) 676 Particles, Strings and the Early Universe. The work of B.H. is partially supported by Grant No. 615203 from the European Research Council under the FP7. The work of R.R. is supported in part by the US Department of Energy under DOE Grant No. de-sc0013699 . The work of A.A.T. is supported by the ERC Advanced Grant No. 290456 , the STFC Grant ST/J0003533/1 and by the Russian Science Foundation Grant 14-42-00047 associated with Lebedev Institute.
Publisher Copyright:
© 2015 The Authors.

PY - 2016/2/1

Y1 - 2016/2/1

N2 - We consider the ABF background underlying the η-deformed AdS5×S5 sigma model. This background fails to satisfy the standard IIB supergravity equations which indicates that the corresponding sigma model is not Weyl invariant, i.e. does not define a critical string theory in the usual sense. We argue that the ABF background should still define a UV finite theory on a flat 2d world-sheet implying that the η-deformed model is scale invariant. This property follows from the formal relation via T-duality between the η-deformed model and the one defined by an exact type IIB supergravity solution that has 6 isometries albeit broken by a linear dilaton. We find that the ABF background satisfies candidate type IIB scale invariance conditions which for the R-R field strengths are of the second order in derivatives. Surprisingly, we also find that the ABF background obeys an interesting modification of the standard IIB supergravity equations that are first order in derivatives of R-R fields. These modified equations explicitly depend on Killing vectors of the ABF background and, although not universal, they imply the universal scale invariance conditions. Moreover, we show that it is precisely the non-isometric dilaton of the T-dual solution that leads, after T-duality, to modification of type II equations from their standard form. We conjecture that the modified equations should follow from κ-symmetry of the η-deformed model. All our observations apply also to η-deformations of AdS3×S3×T4and AdS2×S2×T6models.

AB - We consider the ABF background underlying the η-deformed AdS5×S5 sigma model. This background fails to satisfy the standard IIB supergravity equations which indicates that the corresponding sigma model is not Weyl invariant, i.e. does not define a critical string theory in the usual sense. We argue that the ABF background should still define a UV finite theory on a flat 2d world-sheet implying that the η-deformed model is scale invariant. This property follows from the formal relation via T-duality between the η-deformed model and the one defined by an exact type IIB supergravity solution that has 6 isometries albeit broken by a linear dilaton. We find that the ABF background satisfies candidate type IIB scale invariance conditions which for the R-R field strengths are of the second order in derivatives. Surprisingly, we also find that the ABF background obeys an interesting modification of the standard IIB supergravity equations that are first order in derivatives of R-R fields. These modified equations explicitly depend on Killing vectors of the ABF background and, although not universal, they imply the universal scale invariance conditions. Moreover, we show that it is precisely the non-isometric dilaton of the T-dual solution that leads, after T-duality, to modification of type II equations from their standard form. We conjecture that the modified equations should follow from κ-symmetry of the η-deformed model. All our observations apply also to η-deformations of AdS3×S3×T4and AdS2×S2×T6models.

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U2 - 10.1016/j.nuclphysb.2015.12.012

DO - 10.1016/j.nuclphysb.2015.12.012

M3 - Article

AN - SCOPUS:84953410524

SN - 0550-3213

VL - 903

SP - 262

EP - 303

JO - Nuclear Physics B

JF - Nuclear Physics B

ER -