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Correlation Functions in Integrable Theories: From weak to strong coupling
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2017 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The discovery of integrability in planar N=4 super Yang-Mills and ABJM has enabled a precise study of AdS/CFT. In the past decade integrability has been successfully applied to the spectrum of anomalous dimensions, which can now be obtained at any value of the coupling. However, in order to solve conformal field theories one also needs to understand their structure constants. Recently, there has been great progress in this direction with the all-loop proposal of Basso, Komatsu and Vieira. But there is still much to understand, as it is not yet possible to use that formalism to find structure constants of short operators at strong coupling. It is important to study wrapping corrections and resum them as the TBA did for the spectrum. It is also crucial to obtain perturbative data that can be used to check if the all-loop proposal is correct or if there are new structures that need to be unveiled.

In this thesis we compute several structure constants of short operators at strong coupling, including the structure constant of Konishi with half-BPS operators. Still at strong coupling, we find a relation between the building blocks of superstring amplitudes and the tensor structures allowed by conformal symmetry. We also consider the case of extremal correlation functions and the relation of their poles to mixing with double-trace operators.

We also study three-point functions at weak coupling. We take the OPE limit in a four-point function of half-BPS operators in order to shed some light on the structure of five-loop wrapping corrections of the Hexagon form factors. Finally, we take the first steps in the generalization of the Hexagon programme to other theories. We find the non-extremal setup in ABJM and the residual symmetry that it preserves, which we use to fix the two-particle form factor and constrain the four-particle hexagon. Finally, we find that the Watson equations hint at a dressing phase that needs to be further investigated.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2017. , p. 135
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1524
Keyword [en]
Superstring theory, AdS/CFT correspondence, Integrable field theories, Hexagon form factors
National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:uu:diva-320811ISBN: 978-91-554-9929-7 (print)OAI: oai:DiVA.org:uu-320811DiVA: diva2:1091117
Public defence
2017-06-14, Å4001, Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, 13:00 (English)
Opponent
Supervisors
Available from: 2017-05-23 Created: 2017-04-26 Last updated: 2017-06-08
List of papers
1. Computing Three-Point Functions for Short Operators
Open this publication in new window or tab >>Computing Three-Point Functions for Short Operators
2014 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 3, p. 096-Article in journal (Refereed) Published
Abstract [en]

We compute the three-point structure constants for short primary operators of N=4 super Yang-Mills theory to leading order in the inverse coupling by mapping the problem to a flat-space string theory calculation. We check the validity of our procedure by comparing to known results for three chiral primaries. We then compute the three-point functions for any combination of chiral and non-chiral primaries, with the non-chiral primaries all dual to string states at the first massive level. Along the way we find many cancellations that leave us with simple expressions, suggesting that integrability is playing an important role.

National Category
Subatomic Physics
Research subject
Theoretical Physics
Identifiers
urn:nbn:se:uu:diva-218834 (URN)10.1007/JHEP03(2014)096 (DOI)000347830500001 ()
Available from: 2014-02-18 Created: 2014-02-18 Last updated: 2017-12-06Bibliographically approved
2. Three-point correlators from string amplitudes: mixing and Regge spins
Open this publication in new window or tab >>Three-point correlators from string amplitudes: mixing and Regge spins
2015 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 4, article id 134Article in journal (Refereed) Published
Abstract [en]

This paper has two parts. We first compute the leading contribution to the strong-coupling mixing between the Konishi operator and a double-trace operator composed of chiral primaries by using flat-space vertex operators for the string-duals of the operators. We then compute the three-point functions for protected or unprotected scalar operators with higher spin operators on the leading Regge trajectory. Here we see that the nontrivial spatial structures required by conformal invariance arise naturally from the form of the polarization tensors in the vertex operators. We find agreement with recent results extracted from Mellin amplitudes for four-point functions, as well as with earlier supergravity calculations. We also obtain some new results for other combinations of operators.

Keyword
Supersymmetric gauge theory, Superstrings and Heterotic Strings, AdS-CFT Correspondence, Strong Coupling Expansion
National Category
Physical Sciences
Identifiers
urn:nbn:se:uu:diva-255290 (URN)10.1007/JHEP04(2015)134 (DOI)000353519700002 ()
Funder
Swedish Research Council, 2012-3269
Available from: 2015-06-22 Created: 2015-06-15 Last updated: 2017-12-04Bibliographically approved

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