Abstract
The supersymmetrization of curvature squared terms is important in the study of the low-energy limit of compactified superstrings where a distinguished role is played by the Gauss-Bonnet combination, which is ghost-free. In this Letter, we construct its off-shell N=(1,0) supersymmetrization in six dimensions for the first time. By studying this invariant together with the supersymmetric Einstein-Hilbert term, we confirm and extend known results of the α′-corrected string theory compactified to six dimensions. Finally, we analyze the spectrum about the AdS3×S3 solution.
| Original language | English |
|---|---|
| Article number | 111602 |
| Journal | Physical Review Letters |
| Volume | 119 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 13 Sept 2017 |
Bibliographical note
Publisher Copyright:© 2017 American Physical Society.
Funding
The new GB invariant (10) , together with the Riemann [23–26] and scalar curvature squared [44] combinations, allows one to construct all off-shell N = ( 1 , 0 ) curvature squared invariants in six dimensions. These results give the opportunity to extend known supergravity-matter models by including four-derivative invariants. By having full control of the off-shell supersymmetry transformations, one could determine whether Bogomolny-Prasad-Sommerfield solutions of the two-derivative theory are solutions of the four-derivative ones. In this Letter, we studied the AdS 3 × S 3 solution arising from the near horizon limit of the dyonic string. However, we have not checked whether the full dyonic string, interpolating between the AdS 3 × S 3 and Minkowski 6 , is unmodified by the GB invariant. It will be interesting to explore the full solution in the Einstein-Gauss-Bonnet supergravity, from which one can also extract the central charge of the dual 2D superconformal field theories. Compactifications to 4D of the GB invariant are also of interest. For instance, the string-string-string duality observed in the 4D STU model can be extended to include the higher-derivative corrections by reducing the 6D N = ( 1 , 0 ) Einstein-Gauss-Bonnet supergravity on a 2-torus [45] . We are grateful to D. Butter for discussions and collaboration on related projects. We also thank D. Butter, F. F. Gautason, and S. Theisen for feedback and comments on the manuscript. J. N. acknowledges support from GIF, the German–Israeli Foundation for Scientific Research and Development. Y. P. is supported by the Alexander von Humboldt fellowship. The work of G. T.-M. was supported by the Interuniversity Attraction Poles Program initiated by the Belgian Science Policy (P7/37) and in part by COST Action MP1210. The work of M. O. is supported in part by a Marie Curie Cofund Fellowship (No. 116C028). [1] 1 M. B. Green , J. H. Schwarz , and P. C. West , Nucl. Phys. B254 , 327 ( 1985 ). NUPBBO 0550-3213 10.1016/0550-3213(85)90222-6 [2] 2 M. A. Walton , Phys. Rev. D 37 , 377 ( 1988 ). PRVDAQ 0556-2821 10.1103/PhysRevD.37.377 [3] 3a H. Nishino and E. Sezgin , Nucl. Phys. B278 , 353 ( 1986 ); NUPBBO 0550-3213 10.1016/0550-3213(86)90218-X 3b H. Nishino and E. Sezgin Nucl. Phys. 505 , 497 ( 1997 ). NUPBBO 0550-3213 10.1016/S0550-3213(97)00357-X [4] 4 A. Salam and E. Sezgin , Phys. Lett. 147B , 47 ( 1984 ). PYLBAJ 0370-2693 10.1016/0370-2693(84)90589-6 [5] 5 M. Cvetic , G. W. Gibbons , and C. N. Pope , Nucl. Phys. B677 , 164 ( 2004 ). NUPBBO 0550-3213 10.1016/j.nuclphysb.2003.10.016 [6] 6 G. W. Gibbons , R. Gueven , and C. N. Pope , Phys. Lett. B 595 , 498 ( 2004 ). PYLBAJ 0370-2693 10.1016/j.physletb.2004.06.048 [7] 7a K.-i. Maeda and H. Nishino , Phys. Lett. 154B , 358 ( 1985 ); PYLBAJ 0370-2693 10.1016/0370-2693(85)90409-5 7b K.-i. Maeda and H. Nishino Phys. Lett. 158B , 381 ( 1985 ). PYLBAJ 0370-2693 10.1016/0370-2693(85)90437-X [8] 8 G. W. Gibbons and P. K. Townsend , Nucl. Phys. B282 , 610 ( 1987 ). NUPBBO 0550-3213 10.1016/0550-3213(87)90700-0 [9] 9 J. J. Halliwell , Nucl. Phys. B286 , 729 ( 1987 ). NUPBBO 0550-3213 10.1016/0550-3213(87)90461-5 [10] 10 Y. Aghababaie , C. P. Burgess , S. L. Parameswaran , and F. Quevedo , J. High Energy Phys. , 03 ( 2003 ) 032 . JHEPFG 1029-8479 10.1088/1126-6708/2003/03/032 [11] 11 J. de Boer , Nucl. Phys. B548 , 139 ( 1999 ). NUPBBO 0550-3213 10.1016/S0550-3213(99)00160-1 [12] 12 J. R. David , G. Mandal , and S. R. Wadia , Phys. Rep. 369 , 549 ( 2002 ). PRPLCM 0370-1573 10.1016/S0370-1573(02)00271-5 [13] 13 B. Zwiebach , Phys. Lett. 156B , 315 ( 1985 ). PYLBAJ 0370-2693 10.1016/0370-2693(85)91616-8 [14] 14a S. Deser and A. N. Redlich , Phys. Lett. B 176 , 350 ( 1986 ); PYLBAJ 0370-2693 10.1016/0370-2693(86)90177-2 14b S. Deser and A. N. Redlich Phys. Lett. B 186 , 461(E) ( 1987 ). PYLBAJ 0370-2693 10.1016/0370-2693(87)90326-1 [15] 15 I. Antoniadis , S. Ferrara , R. Minasian , and K. S. Narain , Nucl. Phys. B507 , 571 ( 1997 ). NUPBBO 0550-3213 10.1016/S0550-3213(97)00572-5 [16] 16 I. Antoniadis , R. Minasian , S. Theisen , and P. Vanhove , Classical Quantum Gravity 20 , 5079 ( 2003 ). CQGRDG 0264-9381 10.1088/0264-9381/20/23/009 [17] 17 J. T. Liu and R. Minasian , Nucl. Phys. B874 , 413 ( 2013 ). NUPBBO 0550-3213 10.1016/j.nuclphysb.2013.06.002 [18] 18a S. Cecotti , S. Ferrara , L. Girardello , and M. Porrati , Phys. Lett. 164B , 46 ( 1985 ); PYLBAJ 0370-2693 10.1016/0370-2693(85)90028-0 18b S. Theisen , Nucl. Phys. B263 , 687 ( 1986 ); NUPBBO 0550-3213 10.1016/0550-3213(86)90281-6 18c I. L. Buchbinder and S. M. Kuzenko , Nucl. Phys. B308 , 162 ( 1988 ); NUPBBO 0550-3213 10.1016/0550-3213(88)90047-8 18d S. Cecotti , S. Ferrara , L. Girardello , M. Porrati , and A. Pasquinucci , Phys. Rev. D 33 , 2504 ( 1986 ); PRVDAQ 0556-2821 10.1103/PhysRevD.33.2504 18e S. Ferrara , S. Sabharwal , and M. Villasante , Phys. Lett. B 205 , 302 ( 1988 ); PYLBAJ 0370-2693 10.1016/0370-2693(88)91668-1 18f S. Ferrara and M. Villasante , J. Math. Phys. (N.Y.) 30 , 104 ( 1989 ); JMAPAQ 0022-2488 10.1063/1.528576 18g R. Le Du , Eur. Phys. J. C 5 , 181 ( 1998 ). EPCFFB 1434-6044 10.1007/s100529800819 [19] 19 D. Butter , B. de Wit , S. M. Kuzenko , and I. Lodato , J. High Energy Phys. 12 ( 2013 ) 062 . JHEPFG 1029-8479 10.1007/JHEP12(2013)062 [20] 20a M. Ozkan and Y. Pang , J. High Energy Phys. 03 ( 2013 ) 158 ; JHEPFG 1029-8479 10.1007/JHEP03(2013)158 20b M. Ozkan and Y. Pang J. High Energy Phys. 07 ( 2013 ) 152(E) . JHEPFG 1029-8479 10.1007/JHEP07(2013)152 [21] 21 M. Ozkan and Y. Pang , J. High Energy Phys. 08 ( 2013 ) 042 . JHEPFG 1029-8479 10.1007/JHEP08(2013)042 [22] 22 D. Butter , S. M. Kuzenko , J. Novak , and G. Tartaglino-Mazzucchelli , J. High Energy Phys. 02 ( 2015 ) 111 . JHEPFG 1029-8479 10.1007/JHEP02(2015)111 [23] 23 E. Bergshoeff , A. Salam , and E. Sezgin , Phys. Lett. B 173 , 73 ( 1986 ). PYLBAJ 0370-2693 10.1016/0370-2693(86)91233-5 [24] 24 E. Bergshoeff , A. Salam , and E. Sezgin , Nucl. Phys. B279 , 659 ( 1987 ). NUPBBO 0550-3213 10.1016/0550-3213(87)90015-0 [25] 25 H. Nishino and S. J. Gates, Jr. , Phys. Lett. B 173 , 417 ( 1986 ). PYLBAJ 0370-2693 10.1016/0370-2693(86)90407-7 [26] 26 E. Bergshoeff and M. Rakowski , Phys. Lett. B 191 , 399 ( 1987 ). PYLBAJ 0370-2693 10.1016/0370-2693(87)90629-0 [27] 27a E. Bergshoeff , E. Sezgin , and A. Van Proeyen , Nucl. Phys. B264 , 653 ( 1986 ); NUPBBO 0550-3213 10.1016/0550-3213(86)90503-1 27b E. Bergshoeff , E. Sezgin , and A. Van Proeyen Nucl. Phys. 598 , 667(E) ( 2001 ). NUPBBO 0550-3213 10.1016/S0550-3213(01)00006-2 [28] 28 D. Butter , S. M. Kuzenko , J. Novak , and S. Theisen , J. High Energy Phys. 12 ( 2016 ) 072 . JHEPFG 1029-8479 10.1007/JHEP12(2016)072 [29] 29 D. Butter , J. Novak , and G. Tartaglino-Mazzucchelli , J. High Energy Phys. 05 ( 2017 ) 133 . JHEPFG 1029-8479 10.1007/JHEP05(2017)133 [30] 30 L. J. Romans , Nucl. Phys. B269 , 691 ( 1986 ). NUPBBO 0550-3213 10.1016/0550-3213(86)90517-1 [31] 31 F. Coomans and A. Van Proeyen , J. High Energy Phys. 02 ( 2011 ) 049 . JHEPFG 1029-8479 10.1007/JHEP02(2011)049 [32] 32 E. Bergshoeff , F. Coomans , E. Sezgin , and A. Van Proeyen , J. High Energy Phys. 07 ( 2012 ) 011 . JHEPFG 1029-8479 10.1007/JHEP07(2012)011 [33] 33a P. Breitenlohner and M. F. Sohnius , Nucl. Phys. B165 , 483 ( 1980 ); NUPBBO 0550-3213 10.1016/0550-3213(80)90045-0 33b B. de Wit , J. W. van Holten , and A. Van Proeyen , Phys. Lett. 95B , 51 ( 1980 ); PYLBAJ 0370-2693 10.1016/0370-2693(80)90397-4 33c B. de Wit , R. Philippe , and A. Van Proeyen , Nucl. Phys. B219 , 143 ( 1983 ). NUPBBO 0550-3213 10.1016/0550-3213(83)90432-7 [34] 34a M. Zucker , J. High Energy Phys. 08 ( 2000 ) 016 ; JHEPFG 1029-8479 10.1088/1126-6708/2000/08/016 34b T. Kugo and K. Ohashi , Prog. Theor. Phys. 104 , 835 ( 2000 ). PTPKAV 0033-068X 10.1143/PTP.104.835 [35] 35 S. M. Kuzenko and J. Novak , J. High Energy Phys. 05 ( 2014 ) 093 . JHEPFG 1029-8479 10.1007/JHEP05(2014)093 [36] 36 C. Arias , W. D. Linch III , and A. K. Ridgway , J. High Energy Phys. 05 ( 2016 ) 016 . JHEPFG 1029-8479 10.1007/JHEP05(2016)016 [37] 37 P. S. Howe , G. Sierra , and P. K. Townsend , Nucl. Phys. B221 , 331 ( 1983 ). NUPBBO 0550-3213 10.1016/0550-3213(83)90582-5 [38] 38 D. Butter , J. Novak , M. Ozkan , Y. Pang , and G. Tartaglino-Mazzucchelli (to be published). [39] 39a J. M. Maldacena , Int. J. Theor. Phys. 38 , 1113 ( 1999 ) IJTPBM 0020-7748 10.1023/A:1026654312961 39b [ J. M. Maldacena Adv. Theor. Math. Phys. 2 , 231 ( 1998 )]. 1095-0761 10.4310/ATMP.1998.v2.n2.a1 [40] 40 M. J. Duff , S. Ferrara , R. R. Khuri , and J. Rahmfeld , Phys. Lett. B 356 , 479 ( 1995 ). PYLBAJ 0370-2693 10.1016/0370-2693(95)00838-C [41] 41 S. Deger , A. Kaya , E. Sezgin , and P. Sundell , Nucl. Phys. B536 , 110 ( 1998 ). NUPBBO 0550-3213 10.1016/S0550-3213(98)00555-0 [42] 42 H. Nicolai and H. Samtleben , J. High Energy Phys. 09 ( 2003 ) 036 . JHEPFG 1029-8479 10.1088/1126-6708/2003/09/036 [43] 43 W. Li , W. Song , and A. Strominger , J. High Energy Phys. 04 ( 2008 ) 082 . JHEPFG 1029-8479 10.1088/1126-6708/2008/04/082 [44] 44 M. Ozkan , Ph.D. thesis, Texas A&M University , 2013 . [45] 45 M. J. Duff , J. T. Liu , and J. Rahmfeld , Nucl. Phys. B459 , 125 ( 1996 ). NUPBBO 0550-3213 10.1016/0550-3213(95)00555-2
| Funders | Funder number |
|---|---|
| COST Action MP1210 | MP1210, 116C028 |
| Interuniversity Attraction Poles Program | |
| Alexander von Humboldt-Stiftung | |
| German-Israeli Foundation for Scientific Research and Development | |
| Belgian Federal Science Policy Office | P7/37 |