Abstract
In this paper a Penrose limit is constructed for type IIB AdS6 × S2 × Σ supergravity solutions. These solutions are dual to five dimensional SCFTs related to (p,q) five brane webs, which can often be described in terms of long quiver gauge theories. The null geodesic from which the Penrose limit is constructed is localized at a unique point on the two dimensional Riemann surface Σ, where the AdS6 and S2 metric factors are extremal. The resulting pp-wave spacetime takes a universal form. The world sheet action of the Green-Schwarz string is quadratic in the light cone gauge and the spectrum of string excitations is obtained.
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R. Penrose, Any space-time has a plane wave as a limit, in Differential geometry and relativity, Springer, Dordrecht, The Netherlands (1976), pg. 271.
R. Güven, Plane waves in effective field theories of superstrings, Phys. Lett. B 191 (1987) 275 [INSPIRE].
K. Sfetsos, Gauging a nonsemisimple WZW model, Phys. Lett. B 324 (1994) 335 [hep-th/9311010] [INSPIRE].
K. Sfetsos and A. A. Tseytlin, Four-dimensional plane wave string solutions with coset CFT description, Nucl. Phys. B 427 (1994) 245 [hep-th/9404063] [INSPIRE].
J. M. Figueroa-O’Farrill and G. Papadopoulos, Homogeneous fluxes, branes and a maximally supersymmetric solution of M-theory, JHEP 08 (2001) 036 [hep-th/0105308] [INSPIRE].
M. Blau, J. M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, Penrose limits and maximal supersymmetry, Class. Quant. Grav. 19 (2002) L87 [hep-th/0201081] [INSPIRE].
M. Blau, J. M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, A new maximally supersymmetric background of IIB superstring theory, JHEP 01 (2002) 047 [hep-th/0110242] [INSPIRE].
D. E. Berenstein, J. M. Maldacena and H. S. Nastase, Strings in flat space and pp waves from N = 4 super Yang-Mills, JHEP 04 (2002) 013 [hep-th/0202021] [INSPIRE].
R. R. Metsaev, Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background, Nucl. Phys. B 625 (2002) 70 [hep-th/0112044] [INSPIRE].
R. R. Metsaev and A. A. Tseytlin, Exactly solvable model of superstring in Ramond-Ramond plane wave background, Phys. Rev. D 65 (2002) 126004 [hep-th/0202109] [INSPIRE].
S. Mizoguchi, T. Mogami and Y. Satoh, Penrose limits and Green-Schwarz strings, Class. Quant. Grav. 20 (2003) 1489 [hep-th/0209043] [INSPIRE].
N. R. Constable et al., PP wave string interactions from perturbative Yang-Mills theory, JHEP 07 (2002) 017 [hep-th/0205089] [INSPIRE].
N. Beisert, C. Kristjansen, J. Plefka, G. W. Semenoff and M. Staudacher, BMN correlators and operator mixing in N = 4 super Yang-Mills theory, Nucl. Phys. B 650 (2003) 125 [hep-th/0208178] [INSPIRE].
M. Spradlin and A. Volovich, Superstring interactions in a pp wave background, Phys. Rev. D 66 (2002) 086004 [hep-th/0204146] [INSPIRE].
N. R. Constable, D. Z. Freedman, M. Headrick and S. Minwalla, Operator mixing and the BMN correspondence, JHEP 10 (2002) 068 [hep-th/0209002] [INSPIRE].
T. Nishioka and T. Takayanagi, On type IIA Penrose limit and N = 6 Chern-Simons theories, JHEP 08 (2008) 001 [arXiv:0806.3391] [INSPIRE].
J. Gomis and H. Ooguri, Penrose limit of N = 1 gauge theories, Nucl. Phys. B 635 (2002) 106 [hep-th/0202157] [INSPIRE].
M. Cvetič, H. Lü and C. N. Pope, M theory pp waves, Penrose limits and supernumerary supersymmetries, Nucl. Phys. B 644 (2002) 65 [hep-th/0203229] [INSPIRE].
M. Cvetič, H. Lü and C. N. Pope, Penrose limits, pp waves and deformed M2 branes, Phys. Rev. D 69 (2004) 046003 [hep-th/0203082] [INSPIRE].
U. Gürsoy, C. Núñez and M. Schvellinger, RG flows from Spin(7), CY 4-fold and HK manifolds to AdS, Penrose limits and pp waves, JHEP 06 (2002) 015 [hep-th/0203124] [INSPIRE].
E. D’Hoker, M. Gutperle, A. Karch and C. F. Uhlemann, Warped AdS6 × S2 in type IIB supergravity. Part I. Local solutions, JHEP 08 (2016) 046 [arXiv:1606.01254] [INSPIRE].
E. D’Hoker, M. Gutperle and C. F. Uhlemann, Warped AdS6 × S2 in type IIB supergravity. Part II. Global solutions and five-brane webs, JHEP 05 (2017) 131 [arXiv:1703.08186] [INSPIRE].
V. G. Kac, Lie superalgebras, Adv. Math. 26 (1977) 8 [INSPIRE].
W. Nahm, Supersymmetries and their representations, Nucl. Phys. B 135 (1978) 149 [INSPIRE].
S. Shnider, The superconformal algebra in higher dimensions, Lett. Math. Phys. 16 (1988) 377 [INSPIRE].
A. Brandhuber and Y. Oz, The D4-D8 brane system and five-dimensional fixed points, Phys. Lett. B 460 (1999) 307 [hep-th/9905148] [INSPIRE].
M. Gutperle and C. F. Uhlemann, Surface defects in holographic 5d SCFTs, JHEP 04 (2021) 134 [arXiv:2012.14547] [INSPIRE].
S. Minwalla, Restrictions imposed by superconformal invariance on quantum field theories, Adv. Theor. Math. Phys. 2 (1998) 783 [hep-th/9712074] [INSPIRE].
C. Cordova, T. T. Dumitrescu and K. Intriligator, Multiplets of superconformal symmetry in diverse dimensions, JHEP 03 (2019) 163 [arXiv:1612.00809] [INSPIRE].
O. Bergman, D. Rodríguez-Gómez and C. F. Uhlemann, Testing AdS6/CFT5 in type IIB with stringy operators, JHEP 08 (2018) 127 [arXiv:1806.07898] [INSPIRE].
M. Gutperle, C. Marasinou, A. Trivella and C. F. Uhlemann, Entanglement entropy vs. free energy in IIB supergravity duals for 5d SCFTs, JHEP 09 (2017) 125 [arXiv:1705.01561] [INSPIRE].
J. G. Russo and A. A. Tseytlin, On solvable models of type IIB superstring in NS-NS and RR plane wave backgrounds, JHEP 04 (2002) 021 [hep-th/0202179] [INSPIRE].
J. Polchinski, String theory. Volume 1: an introduction to the bosonic string, Cambridge University Press, Cambridge, U.K. (2007) [INSPIRE].
M. Cvetič, H. Lü, C. N. Pope and K. S. Stelle, Linearly realised world sheet supersymmetry in pp wave background, Nucl. Phys. B 662 (2003) 89 [hep-th/0209193] [INSPIRE].
E. D’Hoker, M. Gutperle and C. F. Uhlemann, Warped AdS6 × S2 in type IIB supergravity. Part III. Global solutions with seven-branes, JHEP 11 (2017) 200 [arXiv:1706.00433] [INSPIRE].
C. F. Uhlemann, AdS6/CFT5 with O7-planes, JHEP 04 (2020) 113 [arXiv:1912.09716] [INSPIRE].
M. Fluder and C. F. Uhlemann, Evidence for a 5d F-theorem, JHEP 02 (2021) 192 [arXiv:2011.00006] [INSPIRE].
F. Baume, J. J. Heckman and C. Lawrie, 6d SCFTs, 4d SCFTs, conformal matter, and spin chains, Nucl. Phys. B 967 (2021) 115401 [arXiv:2007.07262].
C. F. Uhlemann, Wilson loops in 5d long quiver gauge theories, JHEP 09 (2020) 145 [arXiv:2006.01142] [INSPIRE].
C. F. Uhlemann, Exact results for 5d SCFTs of long quiver type, JHEP 11 (2019) 072 [arXiv:1909.01369] [INSPIRE].
M. Fluder and C. F. Uhlemann, Precision test of AdS6/CFT5 in type IIB string theory, Phys. Rev. Lett. 121 (2018) 171603 [arXiv:1806.08374] [INSPIRE].
M. Graña, D3-brane action in a supergravity background: the fermionic story, Phys. Rev. D 66 (2002) 045014 [hep-th/0202118] [INSPIRE].
J. H. Schwarz, Covariant field equations of chiral N = 2, D = 10 supergravity, Nucl. Phys. B 226 (1983) 269 [INSPIRE].
S. F. Hassan, T duality, space-time spinors and RR fields in curved backgrounds, Nucl. Phys. B 568 (2000) 145 [hep-th/9907152] [INSPIRE].
Z. W. Chong, H. Lü and C. N. Pope, Rotating strings in massive type IIA supergravity, hep-th/0402202 [INSPIRE].
Y. Lozano, E. Ó Colgáin and D. Rodríguez-Gómez, Hints of 5d fixed point theories from non-Abelian T-duality, JHEP 05 (2014) 009 [arXiv:1311.4842] [INSPIRE].
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Gutperle, M., Klein, N. A Penrose limit for type IIB AdS6 solutions. J. High Energ. Phys. 2021, 73 (2021). https://doi.org/10.1007/JHEP07(2021)073
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DOI: https://doi.org/10.1007/JHEP07(2021)073