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Subject: search.filters.subject.Yang-Mills theory.

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Now showing 1 - 7 of 7
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    A non-perturbative theory of giant gravitons using AdS/CFT
    (2015-05-07) Kemp, Garreth James
    We explore the non-perturbative physics of giant gravitons in type IIB string theory on the AdS5 ⇥ S5 background in this thesis. The gauge theory dual is N = 4 super Yang-Mills theory with a U(N) gauge group. We diagonalise the one and two-loop dilatation operators acting on the restricted Schur polynomial basis. These operators are dual to a system of giant gravitons with strings attached. Hence, we present evidence for integrability in certain non-planar sectors of the gauge theory. In the second half of the thesis, we turn our focus to N = 4 super Yang-Mills theory with an SO(N) gauge group. In this case, the geometry of the dual gravity theory is AdS5 ⇥RP5. The non-planar physics of the SO(N) theory is distinct from that of the U(N) theory. To pursue the goal of searching for non-planar integrability in the SO(N) gauge theory, one might try to generalise the restricted Schur basis to the SO(N) case. We propose such a basis and evaluate their two-point functions exactly in the free theory. Further, we develop techniques to compute correlation functions of multi-trace operators involving two scalar fields exactly. Lastly, we extend these results to the theory with an Sp(N) gauge group.
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    Instantons in D=5 super-Yang-Mills theory
    (2014-07-07) Tahiridimbisoa, Nirina Maurice Hasina
    One of the key goals of string theory is to provide a uni cation of general relativity and quantum eld theory. In the pursuit of this goal it has become clear that the di erent string theories that have been discovered so far are all in fact, partial descriptions of a single theory. At strong coupling a new theory, called M-theory, is the correct description. M-theory includes gravitons, M2-branes and M5-branes. Up to now, the correct description of the M5-brane is outstanding. In this project some proposals for this theory are studied. In particular, there is a proposal that D=5 maximally supersymmetric Yang-Mills theory can be used to provide a description of the world volume physics of the M5-brane. According to this proposal, instantons in D=5 maximally supersymmetric Yang-Mills theory are graviton excitations of the M theory. In this M.Sc dissertation the instanton solutions of D=5 maximally supersymmetric Yang-Mills theory are explored, with the goal of testing the above proposal. The dissertation begins with a review of the uses of instantons in quantum mechanics. In particular, instantons are used to account for tunneling e ects within a path integral approach to quantum mechanics. The lifting of ground state degeneracies as well as the estimation of the lifetime of unstable states using instantons is developed. The quantization of gauge theories is reviewed in detail. The relevance of instantons for a semi-classical study of Yang-Mills theory is explained. Finally, the relevance of instantons for D = 5 maximally supersymmetric Yang-Mills theory is considered.
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    The large-N limit of matrix models and AdS/CFT
    (2014-06-12) Mulokwe, Mbavhalelo
    Random matrix models have found numerous applications in both Theoretical Physics and Mathematics. In the gauge-gravity duality, for example, the dynamics of the half- BPS sector can be fully described by the holomorphic sector of a single complex matrix model. In this thesis, we study the large-N limit of multi-matrix models at strong-coupling. In particular, we explore the significance of rescaling the matrix fields. In order to investigate this, we consider the matrix quantum mechanics of a single Hermitian system with a quartic interaction. We “compactify” this system on a circle and compute the first-order perturbation theory correction to the ground-state energy. The exact ground-state energy is obtained using the Das-Jevicki-Sakita Collective Field Theory approach. We then discuss the multi-matrix model that results from the compactification of the Higgs sector of N = 4 SYM on S4 (or T S3). For the radial subsector, the saddle-point equations are solved exactly and hence the radial density of eigenvalues for an arbitrary number of even Hermitian matrices is obtained. The single complex matrix model is parametrized in terms of the matrix valued polar coordinates and the first-order perturbation theory density of eigenstates is obtained. We make use of the Harish-Chandra- Itzykson-Zuber (HCIZ) formula to write down the exact saddle-point equations. We then give a complementary approach - based on the Dyson-Schwinger (loop) equations formalism - to the saddle-point method. We reproduce the results obtained for the radial (single matrix) subsector. The two-matrix integral does not close on the original set of variables and thus we map the system onto an auxiliary Penner-type two matrix model. In the absence of a logarithmic potential we derive a radial hemispherical density of eigenvalues. The system is regulated with a logarithm potential, and the Dobroliubov-Makeenko-Semenoff (DMS) loop equations yield an equation of third degree that is satisfied by the generating function. This equation is solved at strong coupling and, accordingly, we obtain the radial density of eigenvalues.
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    Non-planar Ads/CFT from group representation theory
    (2014-06-12) Smith, Stephanie
    In this thesis we explore certain limits of the AdS/CFT correspondence for integrability. This is done by calculating the action of the dilatation operator on operators known as restricted Schur polynomials, which are AdS/CFT dual to D3-branes known as giant gravitons. We focus on operators in N = 4 super-Yang-Mills theory, which is dual to type IIB string theory on an AdS5×S5 background. We find that, in various cases, this theory is integrable in a large N non-planar limit.
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    Brane states and group representation theory
    (2014-01-14) Nokwara, Nkululeko
    A complete understanding of quantum gravity remains an open problem. However, the AdS/CFT correspondence which relates quantum eld theories that enjoy conformal symmetry to theories of (quantum) gravity is proving to be a useful tool in shedding light on this formidable problem. Recently developed group representation theoretic methods have proved useful in understanding the large N; but non-planar limit of N = 4 supersymmetric Yang-Mills theory. In this work, we study operators that are dual to excited giant gravitons, which corresponds to a sector of N = 4 super Yang-Mills theory that is described by a large N; but non-planar limit. After a brief review of the work done in the su (2) sector, we compute the spectrum of anomalous dimensions in the su (2) sector of the Leigh-Strassler deformed theory. The result resembles the spectrum of a shifted harmonic oscillator. We then explain how to construct restricted Schur polynomials built using both fermionic and bosonic elds which transform in the adjoint of the gauge group U (N) : We show that these operators diagonalise the free eld two point function to all orders in 1=N: As an application of our new operators, we study the action of the one-loop dilatation operator in the su (2,3) sector in a large N; but non-planar limit of N = 4 super Yang-Mills theory. As in the su (2) case, the resulting spectrum matches the spectrum of a set of decoupled oscillators. Finally, in an appendix, we study the action of the one-loop dilatation operator in an sl (2) sector of N = 4 super Yang-Mills theory. Again, the resulting spectrum matches that of a set of harmonic oscillators. In all these cases, we nd that the action of the dilatation operator is diagonalised by a double coset ansatz.
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    Giant graviton oscillators
    (2013-08-07) Dessein, Matthias
    We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach to the computation and manipulation of the symmetric group operators appearing in the restricted Schur polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a compact world volume. We find considerable evidence that the dilatation operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in N = 4 super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but non-planar limits.
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    Giant graviton oscillators
    (2013-07-30) Mathwin, C. R.
    We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach to the computation and manipulation of the symmetric group operators appearing in the restricted Schur polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a compact world volume. Generalzing previous results, we find considerable evidence that the dilatation operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in N = 4 super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but non-planar limits.