arXiv subjects

Kayleigh Mathieson

Publications and source records attributed to Kayleigh Mathieson.

4 recordsLinked to original sources

arXiv2025

To gauge or to double gauge? Matrix models, global symmetry, and black hole cohomologies

We study the structure of the Hilbert space of gauged matrix models with a global symmetry. In the first part of the paper, we focus on bosonic matrix models with $U(2)$ gauge group and $SO(d)$ global symmetry, and consider singlets under both the gauge and global symmetry. We show how such "double-gauged'' matrix models can be described in terms of a simpler $SO(3)$ single-matrix model. In the second part of the paper, we consider the so-called BMN subsector of the $\mathcal{N}=4$ $SU(N)$ super Yang-Mills theory, which is closely related to the BMN matrix model. Among the 1/16 BPS operators in this sector, "non-graviton'' operators were recently discovered, which are expected to relate to the microstates of supersymmetric $AdS_5$ black holes. We show that a double gauging of this model, where one projects onto $SU(3)_R$ $R$-symmetry singlets, considerably simplifies the analysis of the non-graviton spectrum. In particular, for low values of $N$, we show that (almost) all graviton operators project out of the spectrum, while important classes of non-graviton operators remain. In the $N=3$ case, we obtain a closed form expression for the superconformal index of singlet non-gravitons, which reveals structural features of their spectrum.

hep-th↗

arXiv2025

Residue sums for superconformal indices

We study superconformal indices of four-dimensional $SU(N)$ gauge theories with $\mathcal{N}=1,2,4$ supersymmetry. The usual representation of a gauge theory index involves multiple contour integrals and reflects the BPS spectrum at zero Yang-Mills coupling. To find an alternative, closed form expression, it is natural to attempt an evaluation of the integrals through residues. However, the presence of non-isolated essential singularities prevents a straightforward evaluation. We show how this difficulty can be resolved by fixing the residual Weyl symmetry of the integral. This allows us to evaluate the residue sums for superconformal indices of $SU(2)$ gauge theories in terms of basic and elliptic hypergeometric series. For the Macdonald index of the $\mathcal{N}=4$ $SU(2)$ super Yang--Mills theory, we show how known transformation formulas for basic hypergeometric series can be used to simplify the residue sum. We observe that the simplified form encodes features of the BPS spectrum at non-zero coupling and suggests the absence of fortuitous or non-graviton operators in the Macdonald sector. Furthermore, we evaluate the residue sums for the Macdonald and full superconformal indices of a general class of $SU(2)$ gauge theories. In the process, we find various applications to the theory of basic and elliptic hypergeometric integrals, including a convergent residue sum for Spiridonov's elliptic beta integral. Finally, we discuss the generalization of our method to higher rank gauge groups and evaluate the $\mathcal{N}=4$ $SU(3)$ Macdonald index in closed form.

hep-th↗

arXiv2019

Hybrid spin-superconducting quantum circuit mediated by deterministically prepared entangled photonic states

In hybrid quantum systems a controllable coupling can be obtained by mediating the interactions with dynamically introduced photons. We propose a hybrid quantum architecture consisting of two nitrogen vacancy center ensembles coupled to a tunable flux qubit; that are contained on the transmission line of a multimode nonlinear superconducting coplanar waveguide resonator with an appended Josephson mixing device. We discuss using entangled propagating microwaves photons, which through our nonlinear wave-mixing procedure are made into macroscopically distinct quantum states. We use these states to steer the system and show that with further amplification we can create a similar photonic state, which has a more distinct reduction of its uncertainty. Furthermore, we show that all of this leads to a lengthened coherence time, a reasonable fidelity which decays to 0.94 and then later increases upward to stabilize at 0.6 as well as a strengthened entanglement.

quant-ph↗

arXiv2019

Experimental Simulation of Hybrid Quantum Systems and Entanglement on a Quantum Computer

We propose the utilization of the IBM Quantum Experience quantum computing system to simulate different scenarios involving common hybrid quantum system components, the Nitrogen Vacancy Centre (NV centre) and the Flux Qubit. We perform a series of the simulation experiments and demonstrate properties of a virtual hybrid system, including its spin relaxation rate and state coherence. In correspondence with experimental investigations we look at the scalability of such systems and show that increasing the number of coupled NV centres decreases the coherence time. We also establish the main error rate as a function of the number of control pulses in evaluating the fidelity of the four qubit virtual circuit with the simulator. Our results show that the virtual system can attain decoherence and fidelity values comparable to what has been reported for experimental investigations of similar physical hybrid systems, observing a coherence time at 0.35 s for a single NV centre qubit and fidelity in the range of 0.82. The work thus establishes an effective simulation test protocol for different technologies to test and analyze them before experimental investigations or as a supplementary measure.

quant-ph↗