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Exact Results in Supersymmetric Field Theories: A dissertation on the defect and deformed
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Quantum field theories (QFTs) are the most precise descriptions of the physical reality that humanity has found. Yet exact predictions are often missing as most computations are notoriously difficult to carry out. One generally resorts to perturbation theory which immediately limits the regime of validity. The need of better computational techniques and a deeper understanding of quantum field theory is evident.

The highly symmetric N=4 SYM theory offers guidance in this quest. The theory's maximal supersymmetry and conformal invariance have allowed for the development of several computational techniques, most notably the AdS/CFT correspondence, supersymmetric localization and applications of integrability. These methods provide the rarity of exact results in a fully interacting QFT and shine light on regimes inaccessible by traditional computations.

The insights drawn from N=4 SYM can be extended into more general settings through deformations and modifications. Three such modifications are the β-deformation, the massive deformation N=2* and N=4 SYM with a defect. This thesis summarizes a number of exact results for these three settings through: i) a spin-chain analogy for two-point functions in the defect N=4 SYM, ii) a vacuum solution for the β-deformed defect N=4 SYM and its spin-chain interpretation of one-point functions, iii) a detailed study of the phase transitions in N=2* applying localization and iv) an adaptation of the Quantum Spectral Curve to explicit calculations of anomalous dimensions in β-deformed N=4 SYM.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2019. , p. 116
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1776
Keywords [en]
AdS/CFT correspondence, integrability, localization, supersymmetric deformations, Quantum Spectral Curve, defect CFT, one-point functions
National Category
Other Physics Topics
Research subject
Theoretical Physics
Identifiers
URN: urn:nbn:se:uu:diva-377042ISBN: 978-91-513-0577-6 (print)OAI: oai:DiVA.org:uu-377042DiVA, id: diva2:1288322
Public defence
2019-04-02, FB53, AlbaNova University Center, Stockholm, 10:15 (English)
Opponent
Supervisors
Available from: 2019-03-12 Created: 2019-02-13 Last updated: 2019-03-18
List of papers
1. Two-point functions of SU(2)-subsector and length-two operators in dCFT
Open this publication in new window or tab >>Two-point functions of SU(2)-subsector and length-two operators in dCFT
2017 (English)In: Physics Letters B, ISSN 0370-2693, E-ISSN 1873-2445, Vol. 773, p. 435-439Article in journal (Refereed) Published
Abstract [en]

We consider a particular set of two-point functions in the setting of N=4SYM with a defect, dual to the fuzzy-funnel solution for the probe D5-D3-brane system. The two-point functions in focus involve a single trace operator in the SU(2)-subsector of arbitrary length and a length-two operator built out of any scalars. By interpreting the contractions as a spin-chain operator, simple expressions were found for the leading contribution to the two-point functions, mapping them to earlier known formulas for the one-point functions in this setting.

Place, publisher, year, edition, pages
ELSEVIER SCIENCE BV, 2017
National Category
Astronomy, Astrophysics and Cosmology
Identifiers
urn:nbn:se:uu:diva-340764 (URN)10.1016/j.physletb.2017.08.059 (DOI)000413294200066 ()
Funder
EU, European Research Council, 341222
Available from: 2018-02-08 Created: 2018-02-08 Last updated: 2019-02-13Bibliographically approved
2. One-point functions in β-deformed N=4 SYM with defect
Open this publication in new window or tab >>One-point functions in β-deformed N=4 SYM with defect
2018 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, Vol. 114, p. 1-18Article in journal (Refereed) Published
Abstract [en]

We generalize earlier results on one-point functions in N=4 SYM with a codimension one defect, dual to the D3-D5-brane setup in type IIB string theory on AdS5 ×S5, to a similar setup in the β-deformed version of the theory. The treelevel vacuum expectation values of single-trace operators in the two-scalar-subsector are expressed as overlaps between a matrix product state (MPS) and Bethe states in the corresponding twisted spin-chain picture. We comment on the properties of this MPS and present the simplest analytical overlaps and their behavior in a certain limit (of large k). Importantly, we note that the deformation alters earlier interpretations of the MPS as an integrable boundary state, seemingly obstructing simplifications of the overlaps analogous to the compact determinant formula found in the non-deformed theory. The results are supplemented with some supporting numerical results for operators of length eight with four excitations.

Keywords
AdS-CFT Correspondence, Duality in Gauge Field Theories, Integrable Field Theories, Lattice Integrable Models
National Category
Subatomic Physics
Identifiers
urn:nbn:se:uu:diva-371326 (URN)10.1007/JHEP11(2018)114 (DOI)000450854500001 ()
Funder
EU, European Research Council, 341222
Note

ArXiv ePrint: 1804.09514

Available from: 2018-12-20 Created: 2018-12-20 Last updated: 2019-06-26Bibliographically approved
3. N = 2* Phase Transitions and Holography
Open this publication in new window or tab >>N = 2* Phase Transitions and Holography
(English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479Article in journal (Refereed) Submitted
National Category
Other Physics Topics
Identifiers
urn:nbn:se:uu:diva-377040 (URN)
Available from: 2019-02-13 Created: 2019-02-13 Last updated: 2019-02-13
4. The fate of the Konishi multiplet in the 𝛽-deformed Quantum Spectral Curve
Open this publication in new window or tab >>The fate of the Konishi multiplet in the 𝛽-deformed Quantum Spectral Curve
(English)Manuscript (preprint) (Other academic)
National Category
Other Physics Topics
Identifiers
urn:nbn:se:uu:diva-377041 (URN)
Available from: 2019-02-13 Created: 2019-02-13 Last updated: 2019-02-13

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