High Energy Physics Theory

We study the modular symmetry on magnetized toroidal orbifolds with Scherk-Schwarz phases. In particular, we investigate finite modular flavor groups for three-generation modes on magnetized orbifolds. The three-generation modes can be the three-dimensional irreducible representations of covering groups and central extended groups of?NforN=3,4,5,7,8,16, that is, covering groups of?(6(N/2)2)forN=even and central extensions ofPSL(2,ZN)forN=odd. We also study anomaly behaviors.

We study the parity-odd sector of 3-point functions comprising of scalar operators and conserved currents in conformal field theories in momentum space. We use momentum space conformal Ward identities as well as spin-raising and weight-shifting operators to fix the form of these correlators. We discuss in detail the regularisation of divergences and their renormalisation using specific counter-terms.

We study monodromy defects inO(N)symmetric scalar field theories inddimensions. After a Weyl transformation, a monodromy defect may be described by placing the theory onS1?Hd??, whereHd??is the hyperbolic space, and imposing on the fundamental fields a twisted periodicity condition alongS1. In this description, the codimension two defect lies at the boundary ofHd??. We first study the general monodromy defect in the free field theory, and then develop the largeNexpansion of the defect in the interacting theory, focusing for simplicity on the case ofNcomplex fields with a one-parameter monodromy condition. We also use theϵ-expansion ind=4?��?, providing a check on the largeNapproach. When the defect has spherical geometry, its expectation value is a meaningful quantity, and it may be obtained by computing the free energy of the twisted theory onS1?Hd??. It was conjectured that the logarithm of the defect expectation value, suitably multiplied by a dimension dependent sine factor, should decrease under a defect RG flow. We check this conjecture in our examples, both in the free and interacting case, by considering a defect RG flow that corresponds to imposing alternate boundary conditions on one of the low-lying Kaluza-Klein modes onHd??. We also show that, adapting standard techniques from the AdS/CFT literature, theS1?Hd??setup is well suited to the calculation of the defect CFT data, and we discuss various examples, including one-point functions of bulk operators, scaling dimensions of defect operators, and four-point functions of operator insertions on the defect.

We compute the entanglement entropy in a two dimensional conformal field theory at finite size and finite temperature in the large central charge limit via the replica trick. We point out that the correlation function of twist operators commonly used to calculate entanglement entropy is not applicable to the torus case and it is necessary to compute the full partition function on the replica surface. We first generalize the known monodromy method for the calculation of conformal blocks on the plane to the torus. Then, we derive a monodromy method for the zero-point conformal blocks of the replica partition function. We explain the differences between the two monodromy methods before applying them to the calculation of the entanglement entropy. We find that the contribution of the vacuum exchange dominates the entanglement entropy for a large class of CFTs, leading to universal results in agreement with holographic predictions from the RT formula. While the twist correlator agrees with the replica partition function and the RT formula for small intervals or low temperatures, it cannot reproduce the entanglement entropy phase transition encountered for large intervals and high temperatures.

Recently four-point holographic correlators with arbitrary external BPS operators were constructively derived in [1,2] at tree-level for maximally superconformal theories. In this paper, we capitalize on these theoretical data, and perform a detailed study of their analytic properties. We point out that these maximally supersymmetric holographic correlators exhibit a hidden dimensional reduction structure ? la Parisi and Sourlas. This emergent structure allows the correlators to be compactly expressed in terms of only scalar exchange diagrams in a dimensionally reduced spacetime, where formally both the AdS and the sphere factors have four dimensions less. We also demonstrate the superconformal properties of holographic correlators under the chiral algebra and topological twistings. ForAdS5?S5andAdS7?S4, we obtain closed form expressions for the meromorphic twisted correlators from the maximally R-symmetry violating limit of the holographic correlators. The results are compared with independent field theory computations in 4dN=4SYM and the 6d(2,0)theory, finding perfect agreement. ForAdS4?S7, we focus on an infinite family of near-extremal four-point correlators, and extract various protected OPE coefficients from supergravity. These OPE coefficients provide new holographic predictions to be matched by future supersymmetric localization calculations. In deriving these results, we also develop many technical tools which should have broader applicability beyond studying holographic correlators.

In this work we investigate the presence of magnetic monopoles that engender multimagnetic structures, which arise from an appropriate extension of theSU(2)gauge group. The investigation is based on a modified relativistic theory that contain several gauge and matter fields, leading to a Bogomol'nyi bound and thus to a first order framework, from which stable multimagnetic solutions can be constructed. We illustrate our findings with several examples of stable magnetic monopoles with multimagnetic properties.

We study rotating global AdS solutions in five-dimensional Einstein gravity coupled to a multiplet complex scalar within a cohomogeneity-1 ansatz. The onset of the gravitational and scalar field superradiant instabilities of the Myers-Perry-AdS black hole mark bifurcation points to black resonators and hairy Myers-Perry-AdS black holes, respectively. These solutions are subject to the other (gravitational or scalar) instability, and result in hairy black resonators which contain both gravitational and scalar hair. The hairy black resonators have smooth zero-horizon limits that we call graviboson stars. In the hairy black resonator and graviboson solutions, multiple scalar components with different frequencies are excited, and hence these are multioscillating solutions. The phase structure of the solutions are examined in the microcanonical ensemble, i.e. at fixed energy and angular momenta. It is found that the entropy of the hairy black resonator is never the largest among them. We also find that hairy black holes with higher scalar wavenumbers are entropically dominant and occupy more of phase space than those of lower wavenumbers.

We study a unitary matrix model with Gross-Witten-Wadia weight function and determinant insertions. After some exact evaluations, we characterize the intricate phase diagram. There are five possible phases: an ungapped phase, two different one-cut gapped phases and two other two-cut gapped phases. The transition from the ungapped phase to any gapped phase is third order, but the transition between any one-cut and any two-cut phase is second order. The physics of tunneling from a metastable vacuum to a stable one and of different releases of instantons is discussed. Wilson loops,β-functions and aspects of chiral symmetry breaking are investigated as well. Furthermore, we study in detail the meromorphic deformation of a general class of unitary matrix models, in which the integration contour is not anchored to the unit circle. The ensuing phase diagram is characterized by symplectic singularities and captured by a Hasse diagram.

We studyN=1supersymmetric three-dimensional Quantum Electrodynamics withNftwo-component fermions. Due to the infra-red (IR) softening of the photon, $\ep$-scalar and photino propagators, the theory flows to an interacting fixed point deep in the IR,pE??e2Nf/8, wherepEis the euclidean momentum andethe electric charge. At next-to-leading order in the1/Nf-expansion, we find that the flow of the dimensionless effective coupling constant $\overline{\al}$ is such that: $\overline{\al} \ra 8/\big(N_f \,(1+C/N_f)\big) \approx (8/N_f)(1-0.4317/N_f)$ whereC=2(12???2)/?2. Hence, the non-trivial IR fixed point is stable with respect to quantum corrections. Various properties of the theory are explored and related via a mapping to the ones of aN=1model of super-graphene. In particular, we derive the interaction correction coefficient to the optical conductivity of super-graphene,Csg=(12???2)/(2?)=0.3391, which is six times larger than in the non-supersymmetric case,Cg=(92???2)/(18?)=0.0561.

We consider the baby Skyrme model in a physically motivated limit of reaching the restricted or BPS baby Skyrme model, which is a model that enjoys area-preserving diffeomorphism invariance. The perturbation consists of the kinetic Dirichlet term with a small coefficientϵas well as the standard pion mass term, with coefficientϵm21. The pions remain lighter than the soliton for anyϵand therefore the model is physically acceptable, even in theϵ??limit. The version of the BPS baby Skyrme model we use has BPS solutions with Gaussian tails. We perform full numerical computations in theϵ??limit and even reach the strictϵ=0case, finding new nontrivial BPS solutions, for which we do not yet know the analytic form.