Browsing by Author "Murugan, Jeff"

Now showing 1 - 8 of 8
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    A study of vortex lattices and pulsar glitches
    (2019) Nkomozake, Thando; Weltman, Amanda; Murugan, Jeff
    In this project we study the three fundamental theories that explain the phenomenon of superconductivity: The London theory, the Ginzburg-Landau theory and the BCS theory. We review works by several authors who utilized these theories as the basis for their investigation. In our literature review we study the behavior of single and multivortex states in mesoscopic thin superconducting discs whose dimensions are comparable to the penetration depth λ and the coherence length ξ of a superconductor. We learn about the types of phase transitions that the vortex configurations undergo and the stability of the resulting states. Our aim is to investigate how vortex configurations reorganize after phase transitions and whether their reorganization releases any energy into the system of vortices in the disc. If so, then what is the precise mechanism through which the released energy is transferred into the disc? We aim to answer this question and generalize the results to neutron star interiors in order to explain and predict the behavior of pulsar glitches.
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    ABJM dibaryon spectroscopy
    (2011) Murugan, Jeff; Prinsloo, Andrea
    We extend the proposal for a detailed map between wrapped D-branes in Anti-de Sitter space and baryon-like operators in the associated dual conformal field theory provided in hep-th/0202150 to the recently formulated AdS4xCP3/ABJM correspondence. In this example, the role of the dibaryon operator of the 3-dimensional CFT is played by a D4-brane wrapping a CP2xCP3. This topologically stable D-brane in the AdS4xCP3 is nothing but one-half of the maximal giant graviton on CP3.
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    Aspects of amplitudes, gravity & complexity
    (2019) Moynihan, Nathan; Murugan, Jeff
    In this thesis, we explore two aspects of modern theoretical physics: scattering amplitudes in gravitational theories and entanglement entropy & complexity in quantum field theory. In part one, we utilise modern scattering amplitude techniques to efficiently calculate the deflection angle of both light and gravity due to the presence of a massive body. We find this to be in complete agreement with the prediction by General relativity. We then construct the scattering amplitudes of massive gravitons to probe the so-called van Dam-Veltman-Zakharov (vDVZ) discontinuity in a purely on-shell manner, which we again find to be in agreement with the usual result. Additionally, we provide a clear physical picture as to the source of the discontinuity that is often obscured by the usual formulation. In part two, we compare three different measures of complexity for a free bosonic QFT: circuit complexity, Fubini-Study complexity, and complexity from the covariance matrix. We show that circuit complexity is the most sensitive of the three, being the only measure able to distinguish between particular physically distinct time-evolved states. Finally, we compute the entanglement entropy, entanglement spectrum, and complexity for various phases of a topological insulator (described in this case by the Su-Schrieffer-Heeger (SSH) model), showing which physical features of the system each quantity captures as it transitions between conformal, topological and massive phases. We show that under certain circumstances, the complexity saturates later than the entanglement entropy, which contradicts the expectation from back hole interiors and AdS/CFT.
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    Beyond the planar limit in ABJM
    (2012) de Mello Koch, Robert; Mohammed, Badr Awad Elseid; Murugan, Jeff; Prinsloo, Andrea
    In this article we consider gauge theories with a U(N) × U(N) gauge group. We provide, for the first time, a complete set of operators built from scalar fields that are in the bi-fundamental of the two groups. Our operators diagonalize the two point function of the free field theory at all orders in 1/N. We then use this basis to investigate nonplanar anomalous dimensions in the ABJM theory. We show that the dilatation operator reduces to a set of decoupled harmonic oscillators, signaling integrability in a large N but non-planar limit of the theory.
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    Classical and quantum integrability in AdS 2/CFT 1
    (2013) Murugan, Jeff; Sundin, Per; Wulff, Linus
    We investigate the type IIA string on AdS 2 × S 2 × T 6 supported by RR-flux which describes the gravitational side of the AdS 2/CFT 1 correspondence. While the four-dimensional part AdS 2 × S 2 can be realized as a supercoset, the full superstring has both coset and non-coset excitations, the latter giving rise to massless worldsheet modes, a somewhat novel feature in AdS/CFT. The string is nevertheless known to be integrable at the classical level. In this paper we perform several computations checking aspects of both classical and quantum string integrability. At the classical level we compute energies for the near BMN string and successfully match these against Bethe ansatz predictions. Furthermore, integrability dictates a magnon dispersion relation which we compare with the poles of loop corrected propagators, at both the one and two-loop level. At one loop, where only tadpole diagrams contribute, we find that the bosonic and fermionic contributions sum up to zero. Under the assumption of worldsheet supersymmetry, we then compute the two-loop sunset diagram in the near flat space limit. As in AdS 5 × S 5 we find that the result fits nicely into the sine-square structure of the dispersion relation.
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    Particle-vortex duality in topological insulators and superconductors
    (2017) Murugan, Jeff; Nastase, Horatiu
    We investigate the origins and implications of the duality between topological insulators and topological superconductors in three and four spacetime dimensions. In the latter, the duality transformation can be made at the level of the path integral in the standard way, while in three dimensions, it takes the form of “self-duality in odd dimensions”. In this sense, it is closely related to the particle-vortex duality of planar systems. In particular, we use this to elaborate on Son’s conjecture that a three dimensional Dirac fermion that can be thought of as the surface mode of a four dimensional topological insulator is dual to a composite fermion.
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    Scattering in AdS2/CFT1 and the BES phase
    (2013) Abbott, Michael C; Murugan, Jeff; Sundin, Per; Wulff, Linus
    We study worldsheet scattering for the type IIA superstring in AdS 2 ×S 2 ×T 6. Using the Green-Schwarz action to quartic order in fermions we take the near-BMN limit, where as in the AdS3/CFT2 case there are both massive and massless excitations. For the massive excitations we compute all possible tree-level processes, and show that these agree with a truncated version of the exact AdS 5 × S 5 S-matrix. We also compute several S-matrix elements involving massless excitations. At one loop we find that the dressing phase is the same Hernándes-López phase appearing in AdS5/CFT4. We see the same phase when calculating this by semiclassical means using the PSU(1, 1 2)/U(1)2 coset sigma model, for which we can also study the scattering of fermions. This supports the conjecture that the all-loop dressing phase is again the BES phase, rather than a new phase like that seen in AdS3/CFT2.
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    The gravity of modern amplitudes: using on-shell scattering amplitudes to probe gravity
    Burger, Daniel Johannes; Murugan, Jeff; Weltman, Amanda
    In this thesis, we explore the use of on-shell scattering amplitudes as a way to understand various gravitational phenomena. We show that amplitudes are a viable way of studying certain aspects of gravity and showcase three such novel results here. First is the computation of the deflection angle of both light and gravitational waves due to a massive static body. We compute this from a purely on-shell amplitude perspective and find that the result is in complete agreement with the corresponding calculation in General Relativity. The second is the ability to derive classical results from the amplitudes. In this section we use on-shell scattering amplitudes to derive the perturbative metric of a rotating black hole in a generic form of Einstein gravity that has additional terms cubic in the Riemann tensor. We show that the metric we derive reduces to correct static metric in the zero angular momentum limit. We show that at first order in the coupling, the classical potential can be written to all orders in spin as a differential operator acting on the non-rotating potential. Further we compute the classical impulse and scattering angle of such a black hole. The third is the resolution of a classical discontinuity in N = 1 super gravity. Here we use on-shell methods for massive particles and use them to compute the supersymmetric version of the van Damme-Veltman-Zakharov (vDVZ) discontinuity. We construct the amplitudes of massive gravitinos (the superpartner of massive gravitons) and show that in the massless limit of the gravitinos there is the same discontinuity as found in massive gravity. This method sheds light on intricacies of the discontinuity that is obscured when handled classically.