Iranian Journal of Physics Research

Worldsheet boundary conditions in non-Abelian T-dual sigma models with the AdS2 metric

Document Type : Original Article

Author

Ali Eghbali

Azarbaijan Shahid Madani University

https://doi.org/10.47176/ijpr.26.1.32302
Abstract
We show that the AdS2 metric in the presence of a Maxwell field together with a constant dilaton field satisfies the equations of motion of the heterotic string theory. Then, by applying non-Abelian T-duality (here, Poisson-Lie T-duality on a semi-Abelian double), a non-Abelian dual pair for the AdS2 metric is constructed. By using a certain parametrization of the two-dimensional non-Abelian Lie group A2 we construct the original sigma model, which includes the AdS2 metric in the absence of a B-field. It is shown that the dual background constructed by means of the Poisson-Lie T-duality is supported by a B-field and a metric that contains a true singularity. By examining the behavior of the dual metric in the region r=0, it is shown that the metric along with a non-trivial dilaton field and an appropriate Maxwell field satisfy the equations of motion of the heterotic string theory for very small r. Most interestingly, for large r, the dual metric approaches the asymptotic solution; in fact, the dual metric is asymptotically AdS2. Finally, we discuss D-branes and the worldsheet boundary conditions defined by a gluing matrix on the AdS2 sigma model. Using the duality map obtained from the canonical transformation description of the Poisson-Lie T-duality for the gluing matrix, which locally defines the properties of the D-brane, we find three different cases of the gluing matrices for the AdS2 sigma model and its dual pair.

Keywords

AdS2 metric
Sigma model
String duality
Worldsheet boundary conditions
D-brane
Subjects
1.       N Sakai and I Senda, Prog. Theo. Phys. 75 (1986) 692.
2.       T H Buscher, Phys. Lett. B 194 (1987) 59.
3.       T H Buscher, Phys. Lett. B 201 (1988) 466.
4.       K Kikkawa and M Yamasaki, Phys. Lett. B 149 (1984) 357.
5.       A Giveon, M. Porrati, and E Rabinovici, Phys. Rep. 224 (1994) 77.
6.       E Alvarez, A Alvarez-Gaume and Y Lozano, Nucl. Phys. B (Proc. Suppl.)  41 (1995) 1.
7.       K Sfetsos, Nucl. Phys. B (Proc. Suppl.)  56 (1997) 302.
8.       K Sfetsos, Nucl. Phys. B 517 (1998) 549.
9.       B E Fridling and A Jevicki, Phys. Lett. B 134 (1984) 70.
10.    K S Narain, M H Sarmadi, and E Witten, Nucl. Phys. B 279 (1987) 369.
11.     X C de la Ossa and F Quevedo, Nucl. Phys. B 403 (1993) 377.
12.     A Giveon and M Rocek, Nucl. Phys. B 42 (1994) 173.
13.    E Alvarez, L Alvarez-Gaume, and Y Lozano, Nucl. Phys. B 424 (1994) 155.
14.    C. Klimcik and P. Severa, Phys. Lett. B 351 (1995) 455.
15.    C. Klimcik, Nucl. Phys. B (Proc. Suppl.)  46 (1996)116.
16.    M A Jafarizadeh, A Rezaei-Aghdam, Phys. Lett. B 458 (1999) 477.
17.    L. Snobl and L. Hlavaty, Int. J. Mod. Phys. A 17 (2002) 4043.
18.    L. Hlavaty and L. Snobl, Mod. Phys. Lett. A 17 (2002) 429.
19.    M A Lledo and V S Varadarajan, Lett. Math. Phys. 45 (1998) 247.
20.    S Majid and E J Beggs, Comm. Math. Phys. 220 (2001) 455.
21.    A Bossard and N Mohammedi, Nucl. Phys. B 619 (2001) 128.
22.    L Hlavaty and L Snobl, J. High Energy Phys. 05 (2004) 010; J. High Energy Phys. 10 (2004) 045.
23.    A Eghbali and A Rezaei-Aghdam, Nucl. Phys. B 899 (2015) 165.
24.    A Eghbali, L Mehran-nia and A Rezaei-Aghdam, Phys. Lett.  B 772 (2017) 791.
25.    M Atazadeh, A Eghbali, Iran. J. Phys. Res. 18 (2018) 23 (persian).
26.    A Eghbali, Phys.  Rev. D 99 (2019) 026001.
27.    A Eghbali, R Naderi and A Rezaei-Aghdam, Eur. Phys. J. C 81 (2021) 68.
28.    A Eghbali, R Naderi and A Rezaei-Aghdam, Eur. Phys. J. C 82 (2022) 580.
29.    Y Sakatani and Y Satoh, J. High Energy Phys. 01 (2024) 150.
30.    A Eghbali and A Rezaei-Aghdam, J. High Energy Phys. 09 (2009) 094.
31.    A Eghbali and A Rezaei-Aghdam, J. High Energy Phys. 01 (2012) 151.
32.    A Eghbali and A Rezaei-Aghdam, Nucl. Phys. B 866 (2013) 26.
33.    A Eghbali and A Rezaei-Aghdam, J. High Energy Phys. 07 (2013) 134.
34.    A Eghbali, J. High Energy Phys. 02 (2015) 025.
35.    A Eghbali, Nucl. Phys. B 958 (2020) 115110.
36.    A Eghbali and A Rezaei-Aghdam, Eur. Phys. J. C 84 (2024) 931.
37.    A Eghbali, M Hosseinpour-Sadid and A Rezaei-Aghdam, J. High Energy Phys. 03 (2024) 040.
38.    A Eghbali, M Hosseinpour-Sadid and A Rezaei-Aghdam, Fortschr. Phys. 74 (2026) e70056.
39.    N Berkovits, M Bershadsky, T Hauer, S Zhukov and B Zwiebach , Nucl. Phys. B 567 (2000) 61.
40.    D Sorokin, A Tseytlin, L Wulff and K Zarembo,  J. Phys. A: Math. Theor. 44 (2011) 275401.
41.    A Eghbali, Fortschr. Phys. 72 (2024) 2400175.
42.    C Klimcik and P Severa, Phys. Lett. B 376 (1996) 82.
43.    C Albertsson and R A Reid-Edwards, J. High Energy Phys. 03 (2007) 004.
44.    Jeffrey A Harvey, et al., “String Theory and Quantum Gravity '92”, Proceedings of the Trieste Spring School and Workshop, ICTP, Trieste, Italy, World Scientific Publishing Company, (1993).
45.    M Nakahara, “Geometry, Topology and Physics”, 2nd Edition, IOP, Bristol and Philadelphia, (2003).
46.     B Zweiebach, “A First Course in String Theory”, Cambridge University Press, (2009).‎

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