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Green-Schwarz superstring on the lattice

Bianchi, L., Bianchi, M. S., Forini, V. ORCID: 0000-0001-9726-1423 , Leder, B. & Vescovi, E. (2016). Green-Schwarz superstring on the lattice. Journal of High Energy Physics, 2016(7), 14. doi: 10.1007/JHEP07(2016)014


We consider possible discretizations for a gauge-fixed Green-Schwarz action of Type IIB superstring. We use them for measuring the action, from which we extract the cusp anomalous dimension of planar N=4 SYM as derived from AdS/CFT, as well as the mass of the two AdS excitations transverse to the relevant null cusp classical string solution. We perform lattice simulations employing a Rational Hybrid Monte Carlo (RHMC) algorithm and two Wilson-like fermion discretizations, one of which preserves the global SO(6) symmetry the model. We compare our results with the expected behavior at various values of g=λ√4π . For both the observables, we find a good agreement for large g, which is the perturbative regime of the sigma-model. For smaller values of g, the expectation value of the action exhibits a deviation compatible with the presence of quadratic divergences. After their non-perturbative subtraction the continuum limit can be taken, and suggests a qualitative agreement with the non-perturbative expectation from AdS/CFT. Furthermore, we detect a phase in the fermion determinant, whose origin we explain, that for small g leads to a sign problem not treatable via standard reweigthing. The continuum extrapolations of the observables in the two different discretizations agree within errors, which is strongly suggesting that they lead to the same continuum limit. Part of the results discussed here were presented earlier in [1].

Publication Type: Article
Additional Information: This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Publisher Keywords: AdS-CFT Correspondence, Lattice Quantum Field Theory, Sigma Models
Subjects: Q Science > QC Physics
Departments: School of Science & Technology > Mathematics
Text - Accepted Version
Available under License Creative Commons Attribution.

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