Abstract
The string coupling of N = 2 supersymmetric compactifications of type II string theory on a Calabi-Yau manifold belongs to the so-called universal dilaton hyper-multiplet, that has four real scalars living on a quaternion-Kähler manifold. Requiring Heisenberg symmetry, which is a maximal subgroup of perturbative isometries, reduces the possible manifolds to a one-parameter family that describes the tree-level effective action deformed by the only possible perturbative correction arising at one-loop level. A similar argument can be made at the level of global supersymmetry where the scalar manifold is hyper-Kähler. In this work, the connection between global and local supersymmetry is explicitly constructed, providing a non-trivial gravity decoupled limit of type II strings already in perturbation theory.
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References
J. Bagger and E. Witten, Matter couplings in N = 2 supergravity, Nucl. Phys. B 222 (1983) 1 [SPIRES].
S. Cecotti, S. Ferrara and L. Girardello, Geometry of type II superstrings and the moduli of superconformal field theories, Int. J. Mod. Phys. A 4 (1989) 2475 [SPIRES].
S. Cecotti, Homogeneous Kähler manifolds and T algebras in N = 2 supergravity and superstrings, Commun. Math. Phys. 124 (1989) 23 [SPIRES].
S. Ferrara and S. Sabharwal, Dimensional reduction of type II superstrings, Class. Quant. Grav. 6 (1989) L77 [SPIRES].
I. Antoniadis, R. Minasian, S. Theisen and P. Vanhove, String loop corrections to the universal hypermultiplet, Class. Quant. Grav. 20 (2003) 5079 [hep-th/0307268] [SPIRES].
I. Antoniadis, S. Ferrara, R. Minasian and K.S. Narain, R 4 couplings in M-and type-II theories on Calabi-Yau spaces, Nucl. Phys. B 507 (1997) 571 [hep-th/9707013] [SPIRES].
N. Ambrosetti, I. Antoniadis, J.P. Derendinger and P. Tziveloglou, Nonlinear supersymmetry, brane-bulk interactions and super-Higgs without gravity, Nucl. Phys. B 835 (2010) 75 [arXiv:0911.5212] [SPIRES].
L. Álvarez-Gaumé and D.Z. Freedman, Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model, Commun. Math. Phys. 80 (1981) 443 [SPIRES].
D.M.J. Calderbank and H. Pedersen, Selfdual Einstein metrics with torus symmetry, J. Diff. Geom. 60 (2002) 485 [math/0105263].
K. Galicki, Quaternionic Kähler and hyperkähler nonlinear σ-models, Nucl. Phys. B 271 (1986) 402 [SPIRES].
K. Galicki, New matter couplings in N = 2 supergravity, Nucl. Phys. B 289 (1987) 573 [SPIRES].
B. de Wit, M. Roček and S. Vandoren, Hypermultiplets, hyperKähler cones and quaternion-Kähler geometry, JHEP 02 (2001) 039 [hep-th/0101161] [SPIRES].
B. de Wit, B. Kleijn and S. Vandoren, Superconformal hypermultiplets, Nucl. Phys. B 568 (2000) 475 [hep-th/9909228] [SPIRES].
A. Swann, Hyperkähler and quaternionic Kähler geometry, Math. Ann. 289 (1991) 421.
K. Galicki, Geometry of the scalar couplings in N = 2 supergravity models, Class. Quant. Grav. 9 (1992) 27 [SPIRES].
A. Karlhede, U. Lindström and M. Roček, Selfinteracting tensor multiplets in N = 2 superspace, Phys. Lett. B 147 (1984) 297 [SPIRES].
S.J. Gates,Jr., C.M. Hull and M. Roček, Twisted multiplets and new supersymmetric nonlinear σ-models, Nucl. Phys. B 248 (1984) 157 [SPIRES].
L. Anguelova, M. Roček and S. Vandoren, Quantum corrections to the universal hypermultiplet and superspace, Phys. Rev. D 70 (2004) 066001 [hep-th/0402132] [SPIRES].
U. Lindström and M. Roček, Scalar tensor duality and N = 1, N = 2 nonlinear σ-models, Nucl. Phys. B 222 (1983) 285 [SPIRES].
W. Siegel, Gauge spinor superfield as a scalar multiplet, Phys. Lett. B 85 (1979) 333 [SPIRES].
S.W. Hawking, Gravitational instantons, Phys. Lett. A 60 (1977) 81 [SPIRES].
G.W. Gibbons and S.W. Hawking, Gravitational multi-instantons, Phys. Lett. B 78 (1978) 430 [SPIRES].
B. de Wit, J.W. van Holten and A. Van Proeyen, Transformation rules of N = 2 supergravity multiplets, Nucl. Phys. B 167 (1980) 186 [SPIRES].
B. de Wit, P.G. Lauwers and A. Van Proeyen, Lagrangians of N = 2 supergravity-matter systems, Nucl. Phys. B 255 (1985) 569 [SPIRES].
P.-Y. Casteill, E. Ivanov and G. Valent, U(1) × U(1) quaternionic metrics from harmonic superspace, Nucl. Phys. B 627 (2002) 403 [hep-th/0110280] [SPIRES].
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Ambrosetti, N., Antoniadis, I., Derendinger, JP. et al. The hypermultiplet with Heisenberg isometry in N = 2 global and local supersymmetry. J. High Energ. Phys. 2011, 139 (2011). https://doi.org/10.1007/JHEP06(2011)139
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DOI: https://doi.org/10.1007/JHEP06(2011)139