Abstract
The classical motion of a Nambu-Goto string in AdS3 spacetime is governed by the generalized sinh-Gordon equation. It can locally be reduced to the sinh-Gordon (shG), cosh-Gordon (chG), or Liouville equation, depending on the value of the scalar curvature of the induced metric. In this paper, I examine solutions that contain both shG-type and chG-type regions. The boundary between these regions moves with the speed of light. I show that near such boundaries (generalized) solitons can be classically pair-produced. The solitons move subluminally (superluminally) in the shG (chG) region on the worldsheet, and they correspond to cusps on the string. A direct energy cascade is observed at the moment of pair-creation.
For the calculations, I use an exact discretization of the equation of motion. The solutions are segmented strings. In this discrete system, pair-production leads to a complete evaporation of the shG region. The final state is a gas of cusps in a chG environment.
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References
J. M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 39 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
T. Ishii and K. Murata, Turbulent strings in AdS/CFT, JHEP 06 (2015) 086 [arXiv:1504.02190] [INSPIRE].
K. Pohlmeyer, Integrable Hamiltonian systems and interactions through quadratic constraints, Commun. Math. Phys. 46 (1976) 207 [INSPIRE].
H. J. De Vega and N. G. Sanchez, Exact integrability of strings in D-Dimensional de Sitter space-time, Phys. Rev. D 47 (1993) 3394 [INSPIRE].
I. Bena, J. Polchinski and R. Roiban, Hidden symmetries of the AdS5 × S5 superstring, Phys. Rev. D 69 (2004) 046002 [hep-th/0305116] [INSPIRE].
S. S. Gubser, I. R. Klebanov and A. M. Polyakov, A semiclassical limit of the gauge/string correspondence, Nucl. Phys. B 636 (2002) 99 [hep-th/0204051] [INSPIRE].
M. Kruczenski, Spiky strings and single trace operators in gauge theories, JHEP 08 (2005) 014 [hep-th/0410226] [INSPIRE].
A. Jevicki, K. Jin, C. Kalousios and A. Volovich, Generating AdS string solutions, JHEP 03 (2008) 032 [arXiv:0712.1193] [INSPIRE].
A. Jevicki and K. Jin, Solitons and AdS string solutions, Int. J. Mod. Phys. A 23 (2008) 2289 [arXiv:0804.0412] [INSPIRE].
N. Dorey and M. Losi, Spiky strings and spin chains, arXiv:0812.1704 [INSPIRE].
A. Jevicki and K. Jin, Moduli dynamics of AdS3 strings, JHEP 06 (2009) 064 [arXiv:0903.3389] [INSPIRE].
N. Dorey and M. Losi, Giant holes, J. Phys. A 43 (2010) 285402 [arXiv:1001.4750] [INSPIRE].
N. Dorey and M. Losi, Spiky strings and giant holes, JHEP 12 (2010) 014 [arXiv:1008.5096] [INSPIRE].
A. Irrgang and M. Kruczenski, Rotating Wilson loops and open strings in AdS3, J. Phys. A 46 (2013) 075401 [arXiv:1210.2298] [INSPIRE].
M. Losi, Spiky strings and the AdS/CFT correspondence, Ph.D. thesis, Cambridge University, Cambridge U.K. (2010) [arXiv:1109.5401] [INSPIRE].
D. Vegh, The broken string in Anti-de Sitter space, JHEP 02 (2018) 045 [arXiv:1508.06637] [INSPIRE].
N. Callebaut, S. S. Gubser, A. Samberg and C. Toldo, Segmented strings in AdS3, JHEP 11 (2015) 110 [arXiv:1508.07311] [INSPIRE].
D. Vegh, Colliding waves on a string in AdS3, arXiv:1509.05033 [INSPIRE].
S. S. Gubser, Evolution of segmented strings, Phys. Rev. D 94 (2016) 106007 [arXiv:1601.08209] [INSPIRE].
S. S. Gubser, S. Parikh and P. Witaszczyk, Segmented strings and the McMillan map, JHEP 07 (2016) 122 [arXiv:1602.00679] [INSPIRE].
D. Vegh, Segmented strings from a different angle, arXiv:1601.07571 [INSPIRE].
D. Vegh, Segmented strings coupled to a B-field, JHEP 04 (2018) 088 [arXiv:1603.04504] [INSPIRE].
D. M. Hofman and J. M. Maldacena, Giant magnons, J. Phys. A 39 (2006) 13095 [hep-th/0604135] [INSPIRE].
A. Bastianello, B. Doyon, G. Watts and T. Yoshimura, Generalized hydrodynamics of classical integrable field theory: the sinh-Gordon model, SciPost Phys. 4 (2018) 045 [arXiv:1712.05687] [INSPIRE].
S. J. Orfanidis, Discrete sine-Gordon equations, Phys. Rev. D 18 (1978) 3822 [INSPIRE].
A. L. Larsen and N. G. Sanchez, Sinh-Gordon, cosh-Gordon and Liouville equations for strings and multistrings in constant curvature space-times, Phys. Rev. D 54 (1996) 2801 [hep-th/9603049] [INSPIRE].
A. Neveu and N. Papanicolaou, Integrability of the classical scalar and symmetric scalar-pseudoscalar contact Fermi interactions in two-dimensions, Commun. Math. Phys. 58 (1978) 31 [INSPIRE].
A. Klotzek and M. Thies, Kink dynamics, sinh-Gordon solitons and strings in AdS3 from the Gross-Neveu model, J. Phys. A 43 (2010) 375401 [arXiv:1006.0324] [INSPIRE].
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Vegh, D. Pair-production of cusps on a string in AdS3. J. High Energ. Phys. 2021, 218 (2021). https://doi.org/10.1007/JHEP03(2021)218
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DOI: https://doi.org/10.1007/JHEP03(2021)218