| 1. |
- Chen-Lin, Xinyi
(författare)
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Non-conformal gauge/string duality : A rigorous case study
- 2017
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The gauge/string duality, a.k.a. the holographic principle is a profound assertion that emerged from string theory. It relates strongly-coupled gauge theories to weakly coupled string theories living in a higher-dimensional curved geometry. Nevertheless, it is a conjecture, and only a few instances of its more concrete form, the AdS/CFT correspondence, are well-understood. The most well-studied example is the duality between N=4 SYM, which is a CFT, and type IIB string theory in AdS5xS5 background. Generalization to less symmetric cases is a must, and the next logical step is to add a mass scale to N=4 SYM, therefore breaking its conformal symmetry and leading to N=2* SYM, the theory we study in this thesis. It is supersymmetric enough to employ the powerful localization method that reduces its partition function to a matrix model. We will see that the mass scale causes non-trivial phase structures in its vacuum configuration, visible in the holographic regime. We will probe them using Wilson loops in different representations of the gauge group. On the other hand, the dual supergravity background was derived by Pilch-Warner, making N=2* theory an explicitly testable non-conformal holographic case, which is a rare example. We will prove that the duality works for the dual observables (string action, D-branes) we managed to compute, even at a quantum-level.
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| 2. |
- Ekhammar, Simon
(författare)
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An Exploration of Q-Systems : From Spin Chains to Low-Dimensional AdS/CFT
- 2023
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The discovery of integrability in the planar limit of the AdS5/CFT4 correspondence has led to impressive progress in the study of string theory and four-dimensional N=4 Super-Yang-Mills. In particular, with the formulation of the Quantum Spectral Curve (QSC) the spectral problem is now solved. The QSC has demonstrated its versatility and usefulness in various other applications, including the study of Wilson lines, conformal bootstrap, and the calculation of structure constants.It would be highly desirable to extend the QSC from AdS5/CFT4 to other instances of the AdS/CFT correspondence, a program so far only fully completed for AdS4/CFT3. Achieving this objective requires a solid understanding of the foundation of the QSC, a so-called analytic Q-system. In this thesis and the included papers, we investigate Q-systems and their algebraic and analytic properties. Inspired by the ODE/IM correspondence we propose Q-systems that encode the conserved charges of integrable models with a simply-laced symmetry algebra. In particular, for the case of D(r) a powerful parameterization of the Q-system using pure spinors is employed to efficiently solve compact rational spin chains and find T-functions solving Hirota equations. The extension from D(r) to the non-simply laced algebra B(2)/C(2) is explained and detailed. While many features are similar the relation between the symmetry of the Q-system and that of the integrable model becomes more intricate. By introducing a new method dubbed Monodromy Bootstrap we construct new Quantum Spectral Curves based on gl(2|2). In particular, one curve is conjectured to describe planar string theory on AdS3 with pure RR-flux. We solve the curve in a weak coupling limit both analytically and numerically.We also discuss the problem of finding the eigenvalue spectrum of operators on the squashed seven-sphere coming from the compactification of eleven-dimensional supergravity. These eigenvalues are of importance for the mass spectrum of fields in AdS4.
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| 3. |
- Flodgren, Nadia, 1995-
(författare)
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Beta functions and multi-scalar gauge theory
- 2023
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this licentiate thesis, we provide the context and background for our work One-loop algebras and fixed flow trajectories in adjoint multi-scalar gauge theory (published in JHEP) on the renormalization group flow for a multi-scalar SU(N) gauge theory. The background consists of a description of renormalization group flow, with a focus on beta functions andhow to find fixed points, and multi-scalar theories. In the article we perform one-loop betafunction calculations in an adjoint, massless, multi-scalar Yang-Mills theory with a quartic scalar interaction, in four dimensions and at large N. We calculate the coupled renormalization group flows for this theory using an algebraic description we develop. The results show that to one-loop order real fixed points in the parameter space of the scalar coupling and gauge coupling do not occur.
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| 4. |
- Widen, Erik, 1986-
(författare)
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Exact Results in Supersymmetric Field Theories : A dissertation on the defect and deformed
- 2019
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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| 5. |
- Giangreco Marotta Puletti, Valentina, 1980-
(författare)
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On string integrability : A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- One of the main topics in the modern String Theory are the conjectured string/gauge (AdS/CFT) dualities. Proving such conjectures is extremely difficult since the gauge and string theory perturbative regimes do not overlap. In this perspective, the discovery of infinitely many conserved charges, i.e. the integrability, in the planar AdS/CFT has allowed us to reach immense progresses in understanding and confirming the duality.The first part of this thesis is focused on the gravity side of the AdS5/CFT4 duality: we investigate the quantum integrability of the type IIB superstring on AdS5 x S5. In the pure spinor formulation we analyze the operator algebra by computing the operator product expansion of the Maurer-Cartan currents at the leading order in perturbation theory. With the same approach at one loop order, we show the path-independence of the monodromy matrix which implies the charge conservation law, strongly supporting the quantum integrability of the string sigma-model. We also verify that the Lax pair field strength remains well-defined at one-loop order being free from UV divergences. The same string sigma-model is analyzed in the Green-Schwarz formalism in the near-flat-space (NFS) limit. Such a limit remarkably simplifies the string world-sheet action but still leaving interesting physics. We use the NFS truncation to show the factorization of the world-sheet S-matrix at one-loop order. This property defines a two-dimensional field theory as integrable: it is the manifestation of the higher conserved charges. Hence, we have explicitly checked their presence at quantum level. The second part is dedicated to the AdS4/CFT3 duality: in particular the type IIA superstring on AdS4 x CP3. We compute the leading quantum corrections to the string energies for string configurations with a large but yet finite angular momentum on CP3 and show that they match the conjectured all-loop Bethe Ansatz equations.
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| 6. |
- Lübcke, Martin, 1975-
(författare)
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Linking Chains Together : String Bits and the Bethe Ansatz
- 2004
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis is divided into two parts. In the first part we focus mainly on certain aspects of the AdS/CFT correspondence. The AdS/CFT correspondence is a proposed duality between Type IIB superstring theory on AdS5 x S5 and N = 4 supersymmetric Yang-Mills theory. In the BMN limit string states located in the center of AdS5 rotate quickly around the equator of the S5 and correspond, in the dual theory, to operators constructed as long chains of sub-operators. This structure of the operators can be formulated as a spin chain and by using the Bethe ansatz their properties can be obtained by solving a set of Bethe equations. Having infinitely many sub-operators, there are methods for solving the Bethe equations in certain sectors. In paper III finite size corrections to the anomalous dimensions in the SU(2) sector are calculated to leading order.Inspired by the chain structure of the corresponding operators, the theory of string bits treats the strings as a discrete sets of points. This theory suffers from the problem of fermion doubling, a general pathology of fermions on a lattice. In paper II we show how to adjust the theory in order to avoid this problem and, in fact, use the fermion doubling to our advantage. The second part of the thesis studies the low energy behaviour of SU(2) Yang-Mills theory in 4 space-time dimensions. In paper I we perform numerical calculations on an effective action for this theory. We propose the existence of a knotted trajectory within the dynamics of this effective action.
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| 7. |
- Medina Rincon, Daniel Ricardo, 1989-
(författare)
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Holographic Wilson Loops : Quantum String Corrections
- 2018
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The gauge-string duality has been one of the most exciting areas in theoretical physics as it connects strongly coupled field theories with weakly interacting strings. The present thesis concerns the study of Wilson loops in this correspondence. Wilson loops are observables arising in many physical situations like the propagation of particles in gauge fields, the problem of confinement, etc. In the gauge-string correspondence these observables have a known physical description at both sides, making them ideal probes for the duality. Remarkable progress from localization has lead to predictions at all orders in the coupling for certain Wilson loop configurations in supersymmetric field theories. Being the string theory weakly interacting, in principle we can use perturbation theory to calculate the corresponding quantities. However, current string calculations have only been successful at leading order and in rare cases, next to leading order. At next to leading order the difficulties encountered include divergences, ambiguous boundary conditions, mismatch with field theory results, etc. The research presented in this thesis aims at a better understanding of these issues. The first calculation presented here concerns the Wilson line in N=2*, a massive deformation of N=4 SYM. The string theory dual to this configuration is a straight line in the type IIB Pilch-Warner background. Using techniques for functional determinants, we computed the 1-loop string partition function obtaining perfect matching with localization. This constitutes a first test of the correspondence at the quantum level for nonconformal theories. The second calculation in this thesis corresponds to the ratio of the latitude and circular Wilson loops in AdS5xS5. An IR anomaly related to the singular nature of the conformal gauge is shown to solve previously found discrepancies with field theory results.
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