Approaching the self-dual point of the sinh-Gordon model
Abstract One of the most striking but mysterious properties of the sinh-Gordon model (ShG) is the b → 1/b self-duality of its S-matrix, of which there is no trace in its Lagrangian formulation. Here b is the coupling appearing in the model’s eponymous hyperbolic cosine present in its Lagrangian, cos...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
SpringerOpen
2021-01-01
|
Series: | Journal of High Energy Physics |
Subjects: | |
Online Access: | https://doi.org/10.1007/JHEP01(2021)014 |
id |
doaj-d61002e9d8be43b9b1c1f5c5bc621262 |
---|---|
record_format |
Article |
spelling |
doaj-d61002e9d8be43b9b1c1f5c5bc6212622021-01-10T12:10:02ZengSpringerOpenJournal of High Energy Physics1029-84792021-01-012021118510.1007/JHEP01(2021)014Approaching the self-dual point of the sinh-Gordon modelRobert Konik0Márton Lájer1Giuseppe Mussardo2CMPMS Dept., Bldg. 734, Brookhaven National LaboratoryWigner Research Centre for PhysicsSISSA and INFN, Sezione di TriesteAbstract One of the most striking but mysterious properties of the sinh-Gordon model (ShG) is the b → 1/b self-duality of its S-matrix, of which there is no trace in its Lagrangian formulation. Here b is the coupling appearing in the model’s eponymous hyperbolic cosine present in its Lagrangian, cosh(bϕ). In this paper we develop truncated spectrum methods (TSMs) for studying the sinh-Gordon model at a finite volume as we vary the coupling constant. We obtain the expected results for b ≪ 1 and intermediate values of b, but as the self-dual point b = 1 is approached, the basic application of the TSM to the ShG breaks down. We find that the TSM gives results with a strong cutoff E c dependence, which disappears according only to a very slow power law in E c . Standard renormalization group strategies — whether they be numerical or analytic — also fail to improve upon matters here. We thus explore three strategies to address the basic limitations of the TSM in the vicinity of b = 1. In the first, we focus on the small-volume spectrum. We attempt to understand how much of the physics of the ShG is encoded in the zero mode part of its Hamiltonian, in essence how ‘quantum mechanical’ vs ‘quantum field theoretic’ the problem is. In the second, we identify the divergencies present in perturbation theory and perform their resummation using a supra-Borel approximate. In the third approach, we use the exact form factors of the model to treat the ShG at one value of b as a perturbation of a ShG at a different coupling. In the light of this work, we argue that the strong coupling phase b > 1 of the Lagrangian formulation of model may be different from what is naïvely inferred from its S-matrix. In particular, we present an argument that the theory is massless for b > 1.https://doi.org/10.1007/JHEP01(2021)014Field Theories in Lower DimensionsIntegrable Field TheoriesNonperturbative Effects |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Robert Konik Márton Lájer Giuseppe Mussardo |
spellingShingle |
Robert Konik Márton Lájer Giuseppe Mussardo Approaching the self-dual point of the sinh-Gordon model Journal of High Energy Physics Field Theories in Lower Dimensions Integrable Field Theories Nonperturbative Effects |
author_facet |
Robert Konik Márton Lájer Giuseppe Mussardo |
author_sort |
Robert Konik |
title |
Approaching the self-dual point of the sinh-Gordon model |
title_short |
Approaching the self-dual point of the sinh-Gordon model |
title_full |
Approaching the self-dual point of the sinh-Gordon model |
title_fullStr |
Approaching the self-dual point of the sinh-Gordon model |
title_full_unstemmed |
Approaching the self-dual point of the sinh-Gordon model |
title_sort |
approaching the self-dual point of the sinh-gordon model |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2021-01-01 |
description |
Abstract One of the most striking but mysterious properties of the sinh-Gordon model (ShG) is the b → 1/b self-duality of its S-matrix, of which there is no trace in its Lagrangian formulation. Here b is the coupling appearing in the model’s eponymous hyperbolic cosine present in its Lagrangian, cosh(bϕ). In this paper we develop truncated spectrum methods (TSMs) for studying the sinh-Gordon model at a finite volume as we vary the coupling constant. We obtain the expected results for b ≪ 1 and intermediate values of b, but as the self-dual point b = 1 is approached, the basic application of the TSM to the ShG breaks down. We find that the TSM gives results with a strong cutoff E c dependence, which disappears according only to a very slow power law in E c . Standard renormalization group strategies — whether they be numerical or analytic — also fail to improve upon matters here. We thus explore three strategies to address the basic limitations of the TSM in the vicinity of b = 1. In the first, we focus on the small-volume spectrum. We attempt to understand how much of the physics of the ShG is encoded in the zero mode part of its Hamiltonian, in essence how ‘quantum mechanical’ vs ‘quantum field theoretic’ the problem is. In the second, we identify the divergencies present in perturbation theory and perform their resummation using a supra-Borel approximate. In the third approach, we use the exact form factors of the model to treat the ShG at one value of b as a perturbation of a ShG at a different coupling. In the light of this work, we argue that the strong coupling phase b > 1 of the Lagrangian formulation of model may be different from what is naïvely inferred from its S-matrix. In particular, we present an argument that the theory is massless for b > 1. |
topic |
Field Theories in Lower Dimensions Integrable Field Theories Nonperturbative Effects |
url |
https://doi.org/10.1007/JHEP01(2021)014 |
work_keys_str_mv |
AT robertkonik approachingtheselfdualpointofthesinhgordonmodel AT martonlajer approachingtheselfdualpointofthesinhgordonmodel AT giuseppemussardo approachingtheselfdualpointofthesinhgordonmodel |
_version_ |
1724343403605393408 |