High Energy Physics Theory

Of the five exceptional groups,E6is considered the most attractive for unification due to the following reasons: (i) it contains bothSpin(10)?U(1)andSU(3)?SU(3)?SU(3)as maximal subgroups, each of which admit embeddings of the Standard Model; (ii) uniquely among the exceptional groups, it admits complex representations; in particular, its 27 dimensional fundamental representation accommodates one generation of left-handed fermions under the usual charge assignments; (iii) all of its representations are anomaly-free. In this master's thesis, written in the spirit of Baez and Huerta's "The Algebra of Grand Unified Theories", we rigorously show how anE6grand unified theory is mathematically constructed. Our modest contribution to the literature includes an explicit check that thatZ4kernel of the homomorphismSpin(10)?U(1)??E6acts trivially on every fermion; we also formulate symmetry breaking, in particular the symmetry breaking of the exoticE6fermions underSpin(10)?�SU(5), using a different approach than the usual Dynkin diagrams: we explicitly embeddedsu(5)?�so(10)?�spin(10)and solve the related eigenvalue problem. Phenomenological aspects of grand unified theories are also discussed.

We considerU(N)kChern-Simons theory onS3in Seifert framing and write down the partition function as a unitary matrix model. In the largekand largeNlimit the eigenvalue density satisfies an upper bound12?λwhereλ=N/(k+N). We study the partition function under saddle point approximation and find that the saddle point equation admits a gapped solution for the eigenvalue density. The on-shell partition function on this solution matches with the partition function in the canonical framing up to a phase. However the eigenvalue density saturates the upper cap at a critical value ofλand ceases to exist beyond that. We find a new phase (called cap-gap phase) in this theory forλbeyond the critical value and see that the on-shell free energy for the cap-gap phase is less than that of the gapped phase. We also check the level-rank duality in the theory and observe that the level-rank dual of the gapped phase is a \emph{capped} phase whereas the cap-gap phase is level-rank dual to itself.

We discuss a particular non-relativistic limit of NS-NS gravity that can be taken at the level of the action and equations of motion, without imposing any geometric constraints by hand. This relies on the fact that terms that diverge in the limit and that come from the Vielbein in the Einstein-Hilbert term and from the kinetic term of the Kalb-Ramond two-form field cancel against each other. This cancelling of divergences is the target space analogue of a similar cancellation that takes place at the level of the string sigma model between the Vielbein in the kinetic term and the Kalb-Ramond field in the Wess-Zumino term. The limit of the equations of motion leads to one equation more than the limit of the action, due to the emergence of a local target space scale invariance in the limit. Some of the equations of motion can be solved by scale invariant geometric constraints. These constraints define a so-called Dilatation invariant String Newton-Cartan geometry.

In this note, we explicitly compute the vacuum expectation value of the commutator of scalar fields in a d-dimensional conformal field theory on the cylinder. We find from explicit calculations that we need smearing not only in space but also in time to have finite commutators except for those of free scalar operators. Thus the equal time commutators of the scalar fields are not well-defined for a non-free conformal field theory, even if which is defined from the Lagrangian. We also have the commutator for a conformal field theory on Minkowski space, instead of the cylinder, by taking the small distance limit.

We show that bulk operators lying between the outermost extremal surface and the asymptotic boundary admit a simple boundary reconstruction in the classical limit. This is the converse of the Python's lunch conjecture, which proposes that operators with support between the minimal and outermost (quantum) extremal surfaces - e.g. the interior Hawking partners - are highly complex. Our procedure for reconstructing this "simple wedge" is based on the HKLL construction, but uses causal bulk propagation of perturbed boundary conditions on Lorentzian timefolds to expand the causal wedge as far as the outermost extremal surface. As a corollary, we establish the Simple Entropy proposal for the holographic dual of the area of a marginally trapped surface as well as a similar holographic dual for the outermost extremal surface. We find that the simple wedge is dual to a particular coarse-grained CFT state, obtained via averaging over all possible Python's lunches. An efficient quantum circuit converts this coarse-grained state into a "simple state" that is indistinguishable in finite time from a state with a local modular Hamiltonian. Under certain circumstances, the simple state modular Hamiltonian generates an exactly local flow; we interpret this result as a holographic dual of black hole uniqueness.

We give a double copy construction for the symmetries of the self-dual sectors of Yang-Mills (YM) and gravity, in the light-cone formulation. We find an infinite set of double copy constructible symmetries. We focus on two families which correspond to the residual diffeomorphisms on the gravitational side. For the first one, we find novel non-perturbative double copy rules in the bulk. The second family has a more striking structure, as a non-perturbative gravitational symmetry is obtained from a perturbatively defined symmetry on the YM side.At null infinity, we find the YM origin of the subset of extended Bondi-Metzner-Sachs (BMS) symmetries that preserve the self-duality condition. In particular, holomorphic large gauge YM symmetries are double copied to holomorphic supertranslations. We also identify the single copy of superrotations with certain non-gauge YM transformations that to our knowledge have not been previously presented in the literature.

This paper describes a generalization of decomposition in orbifolds. In general terms, decomposition states that two-dimensional orbifolds and gauge theories whose gauge groups have trivially-acting subgroups decompose into disjoint unions of theories. However, decomposition can be, at least naively, broken in orbifolds if the orbifold has discrete torsion in the trivially-acting subgroup. (Formally, this breaks finite global one-form symmetries.) Nevertheless, even in such cases, one still sees rudiments of decomposition. In this paper, we generalize decomposition in orbifolds to include such examples of discrete torsion, which we check in numerous examples. Our analysis includes as special cases (and in one sense generalizes) quantum symmetries of abelian orbifolds.

We estimate the net information exchange between adjacent quantum subsystems holographically living on the boundary ofAdSspacetime. The information exchange is a real time phenomenon and only after long time interval it may get saturated. Normally we prepare systems for small time intervals and measure the information exchange over finite interval only. We find that the information flow between entangled subsystems gets reduced if systems are in excited state whereas the ground state allows maximum information flow at any given time. Especially forCFT2we exactly show that a rise in the entropy is detrimental to the information exchange by a quantum dot and vice-versa. We next observe that there is a reduction in circuit (CV) complexity too in the presence of excitations for small times.

We find a late times approximation for the SYK spectral form factor from a largeNsteepest descent version of the path integral over two replica collective fields. Main ingredients are a suitable uv regularization of the two replica kinetic operator, the property of its Fourier transform and some spectral analysis of the four point function two replica ladder kernel.

In this paper, we have constructed a bottom-up holographic model for the color superconductivity (CSC) of the Yang-Mills theory in the context of Einstein-Gauss-Bonnet (EGB) gravity, which allows to study the CSC phase with the color numberNc??. We analyze the Cooper pair condensate in the deconfinement and confinement phases which are dual to the planar GB-RN-AdS black hole and GB-AdS soliton, respectively, with including the backreaction of the matter part. By examining the breakdown of the Breitenlohner-Freedman bound in the background of the planar GB-RN-AdS black hole, we find that the upper bound of the color number with the GB coupling parameterα>0is low in comparison to Einstein gravity where the CSC phase forNc??is not realized. But, with theα<0case, it is possible to observe the Cooper pair condensate forNc??with the reasonable amplitude ofα. This is confirmed and the corresponding phase diagram is found by solving numerically the equations of motion for the gravitational system. In addition, we show that the CSC phase disappears in the confinement phase for the amplitude ofαbelow a certain value which means that beyond that value it may lead to the breakdown region of the EGB gravity in investigating the CSC phase.