Semiclassical quantization of the mixed-flux AdS 3 giant magnon
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Springer
Received: July 22, 2020 Accepted: August 15, 2020 Published: September 16, 2020
Adam Varga Department of Mathematics, School of Mathematics, Computer Science & Engineering, University of London, City, EC1V 0HB London, U.K.
E-mail: [email protected] Abstract: We obtain explicit formulas for the eight bosonic and eight fermionic fluctuations around the mixed-flux generalization of the Hofman-Maldacena giant magnon on AdS3 ×S3 ×T4 and AdS3 ×S3 ×S3 ×S1 . As a check of our results, we confirm that the semiclassical quantization of these fluctuations leads to a vanishing one-loop correction to the magnon energy, as expected from symmetry based arguments. Keywords: AdS-CFT Correspondence, Superstrings and Heterotic Strings ArXiv ePrint: 2006.12080
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)107
JHEP09(2020)107
Semiclassical quantization of the mixed-flux AdS3 giant magnon
Contents 1 Introduction
1 5 6 6 7 8 10 11
3 Fermionic sector 3.1 The fluctuation equations 3.2 Ansatz and reduced equations 3.3 Solutions
11 11 13 15
4 The 1-loop functional determinant 4.1 1-loop correction in AdS3 × S3 × S3 × S1 string theory 4.2 1-loop correction in AdS3 × S3 × T4 string theory
19 21 22
5 Conclusions
23
A Dressing the perturbed BMN string A.1 Review of the SU(2) dressing method A.2 Dressing the unperturbed BMN string A.3 Dressing the perturbed BMN string
25 25 26 27
B Comparison to AdS5 × S5 fluctuations B.1 Bosonic fluctuations B.2 Fermionic fluctuations
30 30 32
C Coefficients in the reduced equations of motion
32
1
Introduction
An important aspect of the AdS5 /CFT4 correspondence [1] is integrability, a hidden symmetry present both on the N = 4 super Yang-Mills gauge theory side [2–4] and AdS5 × S5 type IIB superstring theory side [5–9] of the duality. Interactions in a quantum integrable theory reduce to a series of diffractionless two-body scattering processes, and in the decompactified worldsheet limit the spectrum is solvable using a Bethe Ansatz [10, 11]. Therefore,
–1–
JHEP09(2020)107
2 Bosonic sector 2.1 The stationary giant magnon 2.2 AdS3 fluctuation spectrum 2.3 S3− fluctuation spectrum 2.4 S3+ fluctuation spectrum 2.5 Bosonic modes in AdS3 × S3 × S3 × S1 string theory 2.6 Bosonic modes in AdS3 × S3 × T4 string theory
the main object of interest in (the planar limit of) AdS/CFT is the S-matrix, encoding these two-body scatterings of elementary excitations, or magnons [12]. AdS5 /CFT4 has a psu(2, 2|4) symmetry, and the subalgebra leaving the vacuum invariant is su(2|2)2 . The offshell, centrally extended version of this residual algebra, su(2|2)2c.e. fixes the S-matrix up to an overall phase [13, 14], which then can be calculated from the so-called crossing symmetry [15–19]. These algebraic arguments also determine the magnon dispersion relation to be r p = 1 + 4h2 sin2 , (1.1) 2
Solitons are particle-like solutions of integrable field theories, whose dynamics can be captured by a small number of collective degrees of freedom. Qua
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