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

Arutyunov, G.; Frolov, S.; Hoare, B.; Roiban, R.; Tseytlin, A. A.

doi:10.1016/j.nuclphysb.2015.12.012

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

Abstract

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,more »« less

Authors:

Arutyunov, G.; Frolov, S.;

; Roiban, R.; Tseytlin, A. A.

Publication Date:: Mon Feb 01 00:00:00 EST 2016

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); German Research Foundation (DFG); European Research Council (ERC); Science and Technology Facilities Council (STFC) (United Kingdom); Russian Science Foundation (Russian Federation)

Contributing Org.:: Trinity College, Dublin (Ireland)

OSTI Identifier:: 1234037

Alternate Identifier(s):: OSTI ID: 1364361

Grant/Contract Number:: SC0013699; 615203; 290456; ST/J0003533/1; 14-42-00047

Resource Type:: Published Article

Journal Name:: Nuclear Physics. B

Additional Journal Information:: Journal Name: Nuclear Physics. B Journal Volume: 903 Journal Issue: C; Journal ID: ISSN 0550-3213

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Arutyunov, G., Frolov, S., Hoare, B., Roiban, R., and Tseytlin, A. A. Scale invariance of the η -deformed AdS 5 × S 5 superstring, T-duality and modified type II equations.  Netherlands: N. p., 2016. 
Web.  doi:10.1016/j.nuclphysb.2015.12.012.

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                    Arutyunov, G., Frolov, S., Hoare, B., Roiban, R., & Tseytlin, A. A. Scale invariance of the η -deformed AdS 5 × S 5 superstring, T-duality and modified type II equations.  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2015.12.012

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                    Arutyunov, G., Frolov, S., Hoare, B., Roiban, R., and Tseytlin, A. A. Mon .  
"Scale invariance of the η -deformed AdS 5 × S 5 superstring, T-duality and modified type II equations".  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2015.12.012.

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@article{osti_1234037,

  title        = {Scale invariance of the η -deformed AdS 5 × S 5 superstring, T-duality and modified type II equations},

  author       = {Arutyunov, G. and Frolov, S. and Hoare, B. and Roiban, R. and Tseytlin, A. A.},

  abstractNote = {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 × T4 and AdS2 × S2 × T6 models.},

  doi          = {10.1016/j.nuclphysb.2015.12.012},

  journal      = {Nuclear Physics. B},

  number       = C,

  volume       = 903,

  place        = {Netherlands},

  year         = {Mon Feb 01 00:00:00 EST 2016},

  month        = {Mon Feb 01 00:00:00 EST 2016}

}

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

Abstract

Citation Formats

T-duality, space-time spinors and R–R fields in curved backgrounds journal, February 2000

Renormalisation and composite operators in non-linear σ models journal, January 1987

Dilation shift under duality and torsion of elliptic complex journal, July 1993

AdS 5 × S 5 Mirror Model as a String Sigma Model journal, December 2014

Finiteness and conformal invariance in non-linear sigma models journal, September 1986

T-duality in the Green–Schwarz formalism, and the massless/massive IIA duality map journal, May 2000

Scale and conformal invariance in quantum field theory journal, June 1988

Deformed integrable σ -models, classical R -matrices and classical exchange algebra on Drinfel’d doubles journal, August 2015

Supergravity backgrounds for deformations of AdS n × S n supercoset string models journal, February 2015

β-function approach to the Green-Schwarz superstring journal, June 1988

Consistency between the string background field equation of motion and the vanishing of the conformal anomaly journal, January 1987

Strings in background fields journal, December 1985

β-functions for the Green-Schwarz superstring journal, February 1989

A local renormalization group equation, diffeomorphisms and conformal invariance in sigma models journal, January 1987

Vertex operators in background fields journal, August 1986

Nonlinear models in 2 + ε dimensions journal, September 1985

On integrability of the Yang–Baxter σ-model journal, April 2009

Sigma Model Approach to String Theory journal, April 1989

On space-time interpretation of the coset models in D<26 critical string theory journal, February 1992

η and λ deformations as E -models journal, November 2015

Coupling constants and vertex functions in string theories journal, June 1985

Scale invariance vs conformal invariance journal, March 2015

Yang–Baxter sigma models based on the CYBE journal, April 2015

Duality transformations away from conformal points journal, August 1996

Towards a two-parameter q -deformation of AdS 3 × S 3 × M 4 superstrings journal, February 2015

On integrable deformations of superstring sigma models related to AdSn×Sn supercosets journal, August 2015

Covariant field equations of chiral N = 2 D = 10 supergravity journal, October 1983

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Weyl invariance of the Green-Schwarz heterotic sigma model journal, October 1991

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N = 2 superstrings in a supergravity background journal, November 1985

Supersymmetry and the systematics of T-duality rotations in type-II superstring theories journal, September 2001

Conformal anomaly in a two-dimensional sigma model on a curved background and strings journal, September 1986

Integrable Deformation of the AdS 5 × S 5 Superstring Action journal, February 2014

Duality in the type-II superstring effective action journal, October 1995

An integrable deformation of the AdS 5 × S 5 superstring journal, November 2014

Path-integral derivation of quantum duality in nonlinear sigma-models journal, February 1988

Comments on T-Dualities of Ramond-Ramond Potentials journal, February 2000

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T-duality, space-time spinors and R–R fields in curved backgrounds
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Dilation shift under duality and torsion of elliptic complex
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${AdS}_{5} \times S^{5}$ Mirror Model as a String Sigma Model
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Finiteness and conformal invariance in non-linear sigma models
journal, September 1986

T-duality in the Green–Schwarz formalism, and the massless/massive IIA duality map
journal, May 2000

Scale and conformal invariance in quantum field theory
journal, June 1988

Deformed integrable σ -models, classical R -matrices and classical exchange algebra on Drinfel’d doubles
journal, August 2015

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journal, June 1988

Consistency between the string background field equation of motion and the vanishing of the conformal anomaly
journal, January 1987

Strings in background fields
journal, December 1985

β-functions for the Green-Schwarz superstring
journal, February 1989

A local renormalization group equation, diffeomorphisms and conformal invariance in sigma models
journal, January 1987

Vertex operators in background fields
journal, August 1986

Nonlinear models in 2 + ε dimensions
journal, September 1985

On integrability of the Yang–Baxter σ-model
journal, April 2009

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journal, April 1989

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journal, February 1992

η and λ deformations as $E$ -models
journal, November 2015

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journal, April 2015

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journal, August 1996

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journal, February 2015

On integrable deformations of superstring sigma models related to AdSn×Sn supercosets
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Sigma-model Weyl invariance conditions and string equations of motion
journal, January 1987

Weyl invariance of the Green-Schwarz heterotic sigma model
journal, October 1991

Type IIB superstring action in AdS5 × S5 background
journal, November 1998

N = 2 superstrings in a supergravity background
journal, November 1985

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journal, September 2001

Conformal anomaly in a two-dimensional sigma model on a curved background and strings
journal, September 1986

Integrable Deformation of the ${AdS}_{5} \times S^{5}$ Superstring Action
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Duality in the type-II superstring effective action
journal, October 1995

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journal, November 2014

Path-integral derivation of quantum duality in nonlinear sigma-models
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