T-dualité trong không gian siêu không gian (2, 1)

Journal of High Energy Physics - Tập 2019 - Trang 1-42 - 2019
M. Abou-Zeid1, C. M. Hull2, U. Lindström2,3, M. Roček4
1SUB, Georg-August-Universität Göttingen, Göttingen, Germany
2Theory Group, The Blackett Laboratory, Imperial College London, London, U.K.
3Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden
4C.N. Yang Institute for Theoretical Physics, Stony Brook University, Stony Brook, U.S.A.

Tóm tắt

Chúng tôi tìm ra các quy tắc biến đổi T-dualité cho các mô hình sigma siêu đối xứng hai chiều (2,1) trong không gian siêu (2,1). Kết quả của chúng tôi làm sáng tỏ một số khía cạnh của hình học mô hình sigma (2,1) liên quan đến cuộc thảo luận về T-dualité. Các biến đổi đối xứng phức tạp mà chúng tôi tìm thấy tương đương với các biến đổi đối xứng Buscher thông thường (bao gồm một sự tinh chỉnh quan trọng) cùng với các vi phân hình học. Chúng tôi sử dụng kỹ thuật gauging (bo tròn) của các mô hình sigma trong không gian siêu (2,1), mà chúng tôi đã xem xét và phát triển, tìm được một cách thể hiện rõ ràng, thực tế và hình học cho hành động đã được bo tròn. Chúng tôi thảo luận về các trở ngại khi thực hiện gauging cho các mô hình sigma (2,1), và nhận thấy rằng các trở ngại đối với T-dualité (2,1) yếu hơn đáng kể.

Từ khóa

#T-duality #(2 #1) supersymmetric sigma-models #superspace #gauging #Buscher duality

Tài liệu tham khảo

L. Álvarez-Gaumé and D.Z. Freedman, Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model, Commun. Math. Phys. 80 (1981) 443 [INSPIRE]. S.J. Gates, Jr., C.M. Hull and M. Roček, Twisted multiplets and new supersymmetric nonlinear σ-models, Nucl. Phys. B 248 (1984) 157 [INSPIRE]. P.S. Howe and G. Sierra, Two-dimensional supersymmetric nonlinear σ-models with torsion, Phys. Lett. 148B (1984) 451 [INSPIRE]. C.M. Hull and E. Witten, Supersymmetric σ-models and the heterotic string, Phys. Lett. B 160 (1985) 398 [INSPIRE]. C.M. Hull, σ Model β-functions and String Compactifications, Nucl. Phys. B 267 (1986) 266 [INSPIRE]. C.M. Hull, Lectures on nonlinear sigma models and strings, lectures given at the Vancouver Advanced Research Workshop, published in Super Field Theories, H. Lee and G. Kunstatter, Plenum, New York U.S.A. (1988). P.S. Howe and G. Papadopoulos, Ultraviolet behavior of two-dimensional supersymmetric nonlinear σ models, Nucl. Phys. B 289 (1987) 264 [INSPIRE]. P.S. Howe and G. Papadopoulos, Further remarks on the geometry of two-dimensional nonlinear σ models, Class. Quant. Grav. 5 (1988) 1647 [INSPIRE]. C. Hull and U. Lindström, All (4, 1): σ-models with (4, q) off-shell supersymmetry, JHEP 03 (2017) 042 [arXiv:1611.09884] [INSPIRE]. C. Hull and U. Lindström, All (4, 0): σ-models with (4, 0) off-shell supersymmetry, JHEP 08 (2017) 129 [arXiv:1707.01918] [INSPIRE]. C. Hull and U. Lindström, The generalised complex geometry of (p, q) Hermitian geometries, arXiv:1810.06489 [INSPIRE]. N. Hitchin, Generalized Calabi-Yau manifolds, Quart. J. Math. Oxford Ser. 54 (2003) 281 [math/0209099]. M. Gualtieri, Generalized complex geometry, math/0401221. H. Ooguri and C. Vafa, N = 2 heterotic strings, Nucl. Phys. B 367 (1991) 83 [INSPIRE]. D. Kutasov and E.J. Martinec, New principles for string/membrane unification, Nucl. Phys. B 477 (1996) 652 [hep-th/9602049] [INSPIRE]. D. Kutasov, E.J. Martinec and M. O’Loughlin, Vacua of M-theory and N = 2 strings, Nucl. Phys. B 477 (1996) 675 [hep-th/9603116] [INSPIRE]. D. Kutasov and E.J. Martinec, M-branes and N = 2 strings, Class. Quant. Grav. 14 (1997) 2483 [hep-th/9612102] [INSPIRE]. M.B. Green, World sheets for world sheets, Nucl. Phys. B 293 (1987) 593 [INSPIRE]. C. Hull et al., Generalized Kähler geometry in (2, 1) superspace, JHEP 06 (2012) 013 [arXiv:1202.5624] [INSPIRE]. M. Dine and N. Seiberg, (2, 0) superspace, Phys. Lett. B 180 (1986) 364 [INSPIRE]. A. Giveon, M. Porrati and E. Rabinovici, Target space duality in string theory, Phys. Rept. 244 (1994) 77 [hep-th/9401139] [INSPIRE]. T.H. Buscher, A symmetry of the string background field equations, Phys. Lett. B 194 (1987) 59 [INSPIRE]. T.H. Buscher, Path integral derivation of quantum duality in nonlinear σ-models, Phys. Lett. B 201 (1988) 466 [INSPIRE]. M. Roček and E.P. Verlinde, Duality, quotients and currents, Nucl. Phys. B 373 (1992) 630 [hep-th/9110053] [INSPIRE]. C.M. Hull, A. Karlhede, U. Lindström and M. Roček, Nonlinear σ models and their gauging in and out of superspace, Nucl. Phys. B 266 (1986) 1 [INSPIRE]. A. Kapustin and A. Tomasiello, The general (2, 2) gauged σ-model with three-form flux, JHEP 11 (2007) 053 [hep-th/0610210] [INSPIRE]. W. Merrell, L.A. Pando Zayas and D. Vaman, Gauged (2, 2) σ-models and generalized Kähler geometry, JHEP 12 (2007) 039 [hep-th/0610116] [INSPIRE]. U. Lindström et al., New N = (2, 2) vector multiplets, JHEP 08 (2007) 008 [arXiv:0705.3201] [INSPIRE]. C.M. Hull and B.J. Spence, The gauged nonlinear σ model with Wess-Zumino term, Phys. Lett. B 232 (1989) 204 [INSPIRE]. C.M. Hull and B.J. Spence, The geometry of the gauged σ-model with Wess-Zumino term, Nucl. Phys. B 353 (1991) 379 [INSPIRE]. I. Jack, D.R.T. Jones, N. Mohammedi and H. Osborn, Gauging the general σ model with a Wess-Zumino term, Nucl. Phys. B 332 (1990) 359 [INSPIRE]. C.M. Hull, G. Papadopoulos and B.J. Spence, Gauge symmetries for (p, q) supersymmetric σ-models, Nucl. Phys. B 363 (1991) 593 [INSPIRE]. C.M. Hull, G. Papadopoulos and P.K. Townsend, Potentials for (p, 0) and (1, 1) supersymmetric σ-models with torsion, Phys. Lett. B 316 (1993) 291 [hep-th/9307013] [INSPIRE]. M. Abou Zeid and C.M. Hull, Geometry, isometries and gauging of (2, 1) heterotic σ-models, Phys. Lett. B 398 (1997) 291 [hep-th/9612208] [INSPIRE]. M. Abou Zeid and C.M. Hull, The gauged (2, 1) heterotic σ-model, Nucl. Phys. B 513 (1998) 490 [hep-th/9708047] [INSPIRE]. C.M. Hull, Global aspects of T-duality, gauged σ-models and T-folds, JHEP 10 (2007) 057 [hep-th/0604178] [INSPIRE]. P.M. Crichigno and M. Roček, On gauged linear σ-models with torsion, JHEP 09 (2015) 207 [arXiv:1506.00335] [INSPIRE]. L. Álvarez-Gaumé and D.Z. Freedman, Potentials for the supersymmetric nonlinear σ-model, Commun. Math. Phys. 91 (1983) 87 [INSPIRE]. C.M. Hull, Complex structures and isometries in the (2, 0) supersymmetric nonlinear σ-model, Mod. Phys. Lett. A 5 (1990) 1793 [INSPIRE]. U. Lindström and M. Roček, Scalar tensor duality and N = 1, N = 2 nonlinear σ-models, Nucl. Phys. B 222 (1983) 285 [INSPIRE]. M.T. Grisaru, M. Massar, A. Sevrin and J. Troost, Some aspects of N = (2, 2), D = 2 supersymmetry, Fortsch. Phys. 47 (1999) 301 [hep-th/9801080] [INSPIRE]. U. Lindström et al., T-duality and generalized Kähler geometry, JHEP 02 (2008) 056 [arXiv:0707.1696] [INSPIRE]. W. Merrell and D. Vaman, T-duality, quotients and generalized Kähler geometry, Phys. Lett. B 665 (2008) 401 [arXiv:0707.1697] [INSPIRE]. P.M. Crichigno, The semi-chiral quotient, hyper-Kähler manifolds and T-duality, JHEP 10 (2012) 046 [arXiv:1112.1952] [INSPIRE]. E. Alvarez, L. Álvarez-Gaumé, J.L.F. Barbon and Y. Lozano, Some global aspects of duality in string theory, Nucl. Phys. B 415 (1994) 71 [hep-th/9309039] [INSPIRE]. J.M. Figueroa-O’Farrill and S. Stanciu, Gauged Wess-Zumino terms and equivariant cohomology, Phys. Lett. B 341 (1994) 153 [hep-th/9407196] [INSPIRE]. E.S. Fradkin and A.A. Tseytlin, Quantum equivalence of dual field theories, Annals Phys. 162 (1985) 31 [INSPIRE]. A. Giveon and M. Roček, Introduction to duality, hep-th/9406178 [INSPIRE]. B.E. Fridling and A. Jevicki, Dual representations and ultraviolet divergences in nonlinear σ models, Phys. Lett. 134B (1984) 70 [INSPIRE]. C.M. Hull, Doubled geometry and T-folds, JHEP 07 (2007) 080 [hep-th/0605149] [INSPIRE]. D.M. Belov, C.M. Hull and R. Minasian, T-duality, gerbes and loop spaces, arXiv:0710.5151 [INSPIRE]. C.M. Hull et al., Generalized Kähler geometry and gerbes, JHEP 10 (2009) 062 [arXiv:0811.3615] [INSPIRE]. B. de Wit and P. van Nieuwenhuizen, Rigidly and locally supersymmetric two-dimensional nonlinear σ models with torsion, Nucl. Phys. B 312 (1989) 58 [INSPIRE]. G.W. Delius, M. Roček, A. Sevrin and P. van Nieuwenhuizen, Supersymmetric σ models with nonvanishing Nijenhuis tensor and their operator product expansion, Nucl. Phys. B 324 (1989) 523 [INSPIRE]. J. Bagger and E. Witten, The gauge invariant supersymmetric nonlinear sigma model, Phys. Lett. B 118 (1982) 103. K. Kikkawa and M. Yamasaki, Casimir effects in superstring theories, Phys. Lett. 149B (1984) 357 [INSPIRE]. W. Siegel, Unusual representations of local groups, Phys. Lett. 134B (1984) 318 [INSPIRE]. N.J. Hitchin, A. Karlhede, U. Lindström and M. Roček, Hyper-Kähler metrics and supersymmetry, Commun. Math. Phys. 108 (1987) 535 [INSPIRE]. Y. Lin and S. Tolman, Reduction of twisted generalized Kähler structure, math.DG/0510010. J. Wess, supersymmetry-supergravity, in Topics in quantum field theory and gauge theories, VIII GIFT Int. Seminar on Theoretical Physics, Salamanca, Spain, June 13-19, J.A. de Azcarraga ed., Springer, Germany (1978) [PRINT-77-0885].