zbMATH — the first resource for mathematics

Generalized supergravity equations and generalized Fradkin-Tseytlin counterterm. (English) Zbl 1416.83145
Summary: The generalized Fradkin-Tseytlin counterterm for the (type I) Green-Schwarz superstring is determined for background fields satisfying the generalized supergravity equations (GSE). For this purpose, we revisit the derivation of the GSE based upon the requirement of kappa-symmetry of the superstring action. Lifting the constraint of vanishing bosonic torsion components, we are able to make contact to several different torsion constraints used in the literature. It is argued that a natural geometric interpretation of the GSE vector field that generalizes the dilaton is as the torsion vector, which can combine with the dilatino spinor into the torsion supervector. To find the counterterm, we use old results for the one-loop effective action of the heterotic sigma model. The counterterm is covariant and involves the worldsheet torsion for vanishing curvature, but cannot be constructed as a local functional in terms of the worldsheet metric. It is shown that the Weyl anomaly cancels without imposing any further constraints on the background fields. In the case of ordinary supergravity, it reduces to the Fradkin-Tseytlin counterterm modulo an additional constraint.

83E50 Supergravity
81T50 Anomalies in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
83E30 String and superstring theories in gravitational theory
PDF BibTeX Cite
Full Text: DOI arXiv
[1] G. Arutyunov et al., Scale invariance of the η-deformed AdS_{5} × \(S\)5superstring, T-duality and modified type-II equations, Nucl. Phys.B 903 (2016) 262 [arXiv:1511.05795] [INSPIRE].
[2] F. Delduc, M. Magro and B. Vicedo, An integrable deformation of the AdS_{5} × \(S\)5superstring action, Phys. Rev. Lett.112 (2014) 051601 [arXiv:1309.5850] [INSPIRE].
[3] F. Delduc, M. Magro and B. Vicedo, Derivation of the action and symmetries of the q-deformed AdS_{5} × \(S\)5superstring, JHEP10 (2014) 132 [arXiv:1406.6286] [INSPIRE]. · Zbl 1333.81322
[4] I. Kawaguchi, T. Matsumoto and K. Yoshida, Jordanian deformations of the AdS_{5} × \(S\)5superstring, JHEP04 (2014) 153 [arXiv:1401.4855] [INSPIRE].
[5] R. Borsato and L. Wulff, Target space supergeometry of η and λ-deformed strings, JHEP10 (2016) 045 [arXiv:1608.03570] [INSPIRE]. · Zbl 1390.81412
[6] D. Orlando, S. Reffert, J.-i. Sakamoto and K. Yoshida, Generalized type IIB supergravity equations and non-Abelian classical r-matrices, J. Phys.A 49 (2016) 445403 [arXiv:1607.00795] [INSPIRE].
[7] B. Hoare and A.A. Tseytlin, Homogeneous Yang-Baxter deformations as non-abelian duals of the AdS_{5}σ-model, J. Phys.A 49 (2016) 494001 [arXiv:1609.02550] [INSPIRE].
[8] M. Hong, Y. Kim and E.O. Colgáin, On non-Abelian T-duality for non-semisimple groups, Eur. Phys. J.C 78 (2018) 1025 [arXiv:1801.09567] [INSPIRE].
[9] Borsato, R.; Wulff, L., Non-abelian T-duality and Yang-Baxter deformations of Green-Schwarz strings, JHEP, 08, 027, (2018) · Zbl 1396.83045
[10] C.M. Hull and P.K. Townsend, World sheet supersymmetry and anomaly cancellation in the heterotic string, Phys. Lett.B 178 (1986) 187 [INSPIRE].
[11] S. Elitzur et al., Remarks on non-Abelian duality, Nucl. Phys.B 435 (1995) 147 [hep-th/9409011] [INSPIRE].
[12] L. Wulff and A.A. Tseytlin, κ-symmetry of superstring σ-model and generalized 10d supergravity equations, JHEP06 (2016) 174 [arXiv:1605.04884] [INSPIRE].
[13] P.S. Howe and P.C. West, The complete N = 2, D = 10 supergravity, Nucl. Phys.B 238 (1984) 181 [INSPIRE].
[14] G. Arutyunov, R. Borsato and S. Frolov, Puzzles of η-deformed AdS_{5}× \(S\)5, JHEP12 (2015) 049 [arXiv:1507.04239] [INSPIRE].
[15] Berkovits, N., Super Poincaré covariant quantization of the superstring, JHEP, 04, 018, (2000) · Zbl 0959.81065
[16] N. Berkovits and P.S. Howe, Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring, Nucl. Phys.B 635 (2002) 75 [hep-th/0112160] [INSPIRE].
[17] Mikhailov, A., Cornering the unphysical vertex, JHEP, 11, 082, (2012)
[18] A. Mikhailov, Vertex operators of ghost number three in Type IIB supergravity, Nucl. Phys.B 907 (2016) 509 [arXiv:1401.3783] [INSPIRE]. · Zbl 1336.81074
[19] Sakatani, Y.; Uehara, S.; Yoshida, K., Generalized gravity from modified DFT, JHEP, 04, 123, (2017) · Zbl 1378.83094
[20] J.-i. Sakamoto, Y. Sakatani and K. Yoshida, Weyl invariance for generalized supergravity backgrounds from the doubled formalism, PTEP2017 (2017) 053B07 [arXiv:1703.09213] [INSPIRE].
[21] Baguet, A.; Magro, M.; Samtleben, H., Generalized IIB supergravity from exceptional field theory, JHEP, 03, 100, (2017) · Zbl 1377.83132
[22] L. Wulff, Trivial solutions of generalized supergravity vs. non-Abelian T-duality anomaly, Phys. Lett.B 781 (2018) 417 [arXiv:1803.07391] [INSPIRE]. · Zbl 1398.83128
[23] B. Hoare and A.A. Tseytlin, Type IIB supergravity solution for the T-dual of the η-deformed AdS_{5}× \(S\)5superstring, JHEP10 (2015) 060 [arXiv:1508.01150] [INSPIRE].
[24] C.G. Callan Jr., E.J. Martinec, M.J. Perry and D. Friedan, Strings in background fields, Nucl. Phys.B 262 (1985) 593 [INSPIRE].
[25] E.S. Fradkin and A.A. Tseytlin, Quantum string theory effective action, Nucl. Phys.B 261 (1985) 1 [Erratum ibid.B 269 (1986) 745] [INSPIRE].
[26] C.M. Hull and P.K. Townsend, Finiteness and conformal invariance in nonlinear σ models, Nucl. Phys.B 274 (1986) 349 [INSPIRE].
[27] A.A. Tseytlin, Conformal anomaly in two-dimensional σ-model on curved background and strings, Phys. Lett.B 178 (1986) 34 [INSPIRE].
[28] G.M. Shore, A local renormalization group equation, diffeomorphisms and conformal invariance in σ models, Nucl. Phys.B 286 (1987) 349 [INSPIRE].
[29] A.A. Tseytlin, σ model Weyl invariance conditions and string equations of motion, Nucl. Phys.B 294 (1987) 383 [INSPIRE].
[30] E. Nissimov, S. Pacheva and S. Solomon, Covariant canonical quantization of the Green-Schwarz superstring, Nucl. Phys.B 297 (1988) 349 [INSPIRE].
[31] M.T. Grisaru, H. Nishino and D. Zanon, β-function approach to the Green-Schwarz Superstring, Phys. Lett.B 206 (1988) 625 [INSPIRE].
[32] M.T. Grisaru and D. Zanon, The Green-Schwarz superstring σ model, Nucl. Phys.B 310 (1988) 57 [INSPIRE].
[33] M.T. Grisaru, H. Nishino and D. Zanon, β-functions for the Green-Schwarz superstring, Nucl. Phys.B 314 (1989) 363 [INSPIRE]. · Zbl 0938.81526
[34] P. Pasti and M. Tonin, Covariant quantization of Green-Schwarz heterotic superstring in curved background, Int. J. Mod. Phys.A 4 (1989) 2959 [INSPIRE].
[35] P. Majumdar, R.N. Oerter and A.E. van de Ven, On the conformal anomaly of the Green-Schwarz heterotic string in curved N = 1, D = 10 superspace, Phys. Lett.B 233 (1989) 123 [INSPIRE].
[36] E.A. Bergshoeff and R.E. Kallosh, BRST(1) quantization of the Green-Schwarz superstring, Nucl. Phys.B 333 (1990) 605 [INSPIRE].
[37] S. Bellucci and R.N. Oerter, Weyl invariance of the Green-Schwarz heterotic σ-model, Nucl. Phys.B 363 (1991) 573 [INSPIRE].
[38] Fernández-Melgarejo, JJ; Sakamoto, J-I; Sakatani, Y.; Yoshida, K., Weyl invariance of string theories in generalized supergravity backgrounds, Phys. Rev. Lett., 122, 111602, (2019)
[39] J. Scherk and J.H. Schwarz, Dual models and the geometry of space-time, Phys. Lett.B 52 (1974) 347.
[40] Saa, A., Strings in background fields and Einstein-Cartan theory of gravity, Class. Quant. Grav., 12, l85, (1995) · Zbl 0833.53072
[41] T. Dereli and R.W. Tucker, An Einstein-Hilbert action for axidilaton gravity in four-dimensions, Class. Quant. Grav.12 (1995) L31 [gr-qc/9502018] [INSPIRE].
[42] M. Vasilic and M. Vojinovic, Classical string in curved backgrounds, Phys. Rev.D 73 (2006) 124013 [gr-qc/0610014] [INSPIRE].
[43] D.S. Popovic and B. Sazdovic, The geometrical form for the string space-time action, Eur. Phys. J.C 50 (2007) 683 [hep-th/0701264] [INSPIRE]. · Zbl 1191.81176
[44] F.W. Hehl, J.D. McCrea, E.W. Mielke and Y. Ne’eman, Metric affine gauge theory of gravity: field equations, Noether identities, world spinors and breaking of dilation invariance, Phys. Rept.258 (1995) 1 [gr-qc/9402012] [INSPIRE].
[45] F.W. Hehl and Y.N. Obukhov, Elie Cartans torsion in geometry and in field theory, an essay, Annales Fond. Broglie32 (2007) 157 [arXiv:0711.1535] [INSPIRE].
[46] N. Dragon, Torsion and curvature in extended supergravity, Z. Phys.C 2 (1979) 29 [INSPIRE].
[47] Sorokin, DP, Superbranes and superembeddings, Phys. Rept., 329, 1, (2000) · Zbl 1006.83056
[48] J.A. Shapiro and C.C. Taylor, Superspace supergravity from the superstring, Phys. Lett.B 186 (1987) 69 [INSPIRE].
[49] E. Witten, Twistor-like transform in ten-dimensions, Nucl. Phys.B 266 (1986) 245 [INSPIRE].
[50] J.J. Atick, A. Dhar and B. Ratra, Superspace formulation of ten-dimensional N = 1 supergravity coupled to N = 1 super-Yang-Mills theory, Phys. Rev.D 33 (1986) 2824 [INSPIRE].
[51] L. Bonora, P. Pasti and M. Tonin, Chiral anomalies in higher dimensional supersymmetric theories, Nucl. Phys.B 286 (1987) 150 [INSPIRE].
[52] A. Candiello and K. Lechner, Duality in supergravity theories, Nucl. Phys.B 412 (1994) 479 [hep-th/9309143] [INSPIRE]. · Zbl 1007.83523
[53] S. Bellucci and D. O’Reilly, Non-minimal string corrections and supergravity, Phys. Rev.D 73 (2006) 065009 [hep-th/0603033] [INSPIRE].
[54] S. Bellucci and D. O’Reilly, Complete and consistent non-minimal string corrections to supergravity, arXiv:0806.0509 [INSPIRE].
[55] Lechner, K.; Tonin, M., Superspace formulations of ten-dimensional supergravity, JHEP, 06, 021, (2008)
[56] L. Bonora, P. Pasti and M. Tonin, Superspace formulation of 10D SUGRA+SYM theory à la Green-Schwarz, Phys. Lett.B 188 (1987) 335 [INSPIRE].
[57] L. Bonora et al., Anomaly free supergravity and super-Yang-Mills theories in ten-dimensions, Nucl. Phys.B 296 (1988) 877 [INSPIRE].
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.