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Title: Scale invariance of the η-deformed AdS 5 × S 5 superstring, T-duality and modified type II equations

We consider the ABF background underlying the η-deformed AdS 5 × S 5 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,more » 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 AdS 3 × S 3 × T 4 and AdS 2 × S 2 × T 6 models.« less
 [1] ;  [2] ; ORCiD logo [3] ;  [4] ;  [5]
  1. Univ. of Hamburg (Germany). Inst. of Theoretical Physics. Center for Mathematical Physics
  2. Trinity College, Dublin (Ireland). School of Mathematics. Hamilton Mathematics Inst.
  3. Federal Inst. of Technology (ETH), Zurich (Switzerland). Inst. of Theoretical Physics
  4. Pennsylvania State Univ., University Park, PA (United States). Dept. of Physics
  5. Imperial College, London (United Kingdom). The Blackett Lab.
Publication Date:
Grant/Contract Number:
SC0013699; 615203; 290456; ST/J0003533/1; 14-42-00047
Published Article
Journal Name:
Nuclear Physics. B
Additional Journal Information:
Journal Volume: 903; Journal ID: ISSN 0550-3213
Research Org:
Pennsylvania State Univ., University Park, PA (United States); Imperial College, London (United Kingdom); Federal Inst. of Technology (ETH), Zurich (Switzerland); Univ. of Hamburg (Germany)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); German Research Foundation (DFG); European Research Council (ERC); Science and Technology Facilities Council (STFC) (United Kingdom); Russian Science Foundation (Russian Federation)
Contributing Orgs:
Trinity College, Dublin (Ireland)
Country of Publication:
United States
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1364361