Ground state energy of twisted AdS 3 × S 3 × T 4 superstring and the TBA

Sergey Frolov (Hamilton Mathematics Institute and School of Mathematics, Trinity College, Dublin 2, Ireland) ; Anton Pribytok (Institut für Physik, Humboldt-Universität zu Berlin, Zum Großen Windkanal 2, Berlin, 12489, Germany) ; Alessandro Sfondrini (Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, via Marzolo 8, Padova, 35131, Italy; Istituto Nazionale di Fisica Nucleare, Sezione di Padova, via Marzolo 8, Padova, 35131, Italy; Institute for Advanced Study, Einstein Drive, Princeton, New Jersey, 08540, USA)

We use the lightcone AdS 3 × S 3 × T 4 superstring sigma model with fermions and bosons subject to twisted boundary conditions to find the ground state energy in the semi-classical approximation where effective string tension h and the light-cone momentum L are sent to infinity in such a way that J $$ \mathcal{J} $$ ≡ L/h is kept fixed. We then analyse the ground state energy of the model by means of the mirror TBA equations for the AdS 3 × S 3 × T 4 superstring in the pure RR background. The calculation is performed for small twist μ with L and h fixed, for large L with μ and h fixed, and for small h with μ and L fixed. In these limits the contribution of the gapless worldsheet modes coming from the T 4 bosons and fermions can be computed exactly, and is shown to be proportional to hL/(4L 2 – 1). Comparison with the semi-classical result shows that the TBA equations involve only one Y 0-function for massless excitations but not two as was conjectured before. Some of the results obtained are generalised to the mixed-flux AdS 3 × S 3 × T 4 superstring.

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  "abstracts": [
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      "source": "Springer", 
      "value": "We use the lightcone AdS 3 \u00d7 S 3 \u00d7 T 4 superstring sigma model with fermions and bosons subject to twisted boundary conditions to find the ground state energy in the semi-classical approximation where effective string tension h and the light-cone momentum L are sent to infinity in such a way that   <math> <mi>J</mi> </math>  $$ \\mathcal{J} $$  \u2261 L/h is kept fixed. We then analyse the ground state energy of the model by means of the mirror TBA equations for the AdS 3 \u00d7 S 3 \u00d7 T 4 superstring in the pure RR background. The calculation is performed for small twist \u03bc with L and h fixed, for large L with \u03bc and h fixed, and for small h with \u03bc and L fixed. In these limits the contribution of the gapless worldsheet modes coming from the T 4 bosons and fermions can be computed exactly, and is shown to be proportional to hL/(4L 2 \u2013 1). Comparison with the semi-classical result shows that the TBA equations involve only one Y 0-function for massless excitations but not two as was conjectured before. Some of the results obtained are generalised to the mixed-flux AdS 3 \u00d7 S 3 \u00d7 T 4 superstring."
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Published on:
05 September 2023
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2023 (2023)
Issue 9
Pages 1-29
DOI:
https://doi.org/10.1007/JHEP09(2023)027
arXiv:
2305.17128
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

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