High Energy Physics Theory

We consider the problem of fixing uniform light-cone gauge in the bosonic sector of non-relativistic AdS5?S5string theory found by J. Gomis, J. Gomis and K. Kamimura. We show that if the common AdS5and S5radius is kept large and we expand around a classical string configuration which develops a linear term along the non-relativistic longitudinal spatial direction in the large radius expansion, the light-cone gauge fixed model describes at leading order in the large string tension expansion the dynamics of 8 bosonic free massless scalars in Mink2. We discuss limitations and potential issues of fixing the light-cone gauge in the case where one evades the large radius assumption.

We obtain local numerators satisfying the BCJ color-kinematics duality at one loop for super-Yang-Mills theory in ten dimensions. This is done explicitly for six points via the field-theory limit of the genus-one open superstring correlators for different color orderings, in an analogous manner to an earlier derivation of local BCJ-satisfying numerators at tree level from disk correlators. These results solve an outstanding puzzle from a previous analysis where the six-point numerators did not satisfy the color-kinematics duality.

In a new Weyl 2-spinor approach to Non abelian Gauge Theories, starting with the local U(1) Gauge group of a previous work, we study now the SU(3) case corresponding to quarks (antiquarks) interacting with color fields. The principal difference with the conventional approach is that particle-field interactions are not described by means of potentials but by the field strength magnitudes. Some analytical expressions showing similarities with electrodynamics are obtained. Classical equations that describe the behavior of quarks under gluon fields might be in principle applied to the quark-gluon plasma phase existing during the first instants of the Universe.

A `locally-finite' observable is one for which there is no region of divergence anywhere in the space of real loop momenta; it can therefore be computed (in principle) without regularization. In this work, we prove that all two-loop ratio functions in planar, maximally supersymmetric Yang-Mills theory are locally-finite.

Quantifying entanglement properties of mixed states in quantum field theory via entanglement of purification is a new and challenging subject. In this work, we study entanglement of purification for two intervals far away from each other in the vacuum of a conformal field theory on a lattice. Our main finding is that the decay of the entanglement of purification is enhanced with respect to the mutual information by a logarithm of the distance between the intervals. We explicitly derive this behaviour in the critical Ising spin chain as well as for free fermions. Furthermore, we corroborate it with a general argument valid for any conformal field theory with a gapped spectrum of operators arising as a continuum description of a lattice model. Finally, our methods in conjunction with the strong subadditivity inequality prove that the same dependence on a product of a power and a logarithmic term governs the long-distance asymptotics of the reflected entropy in any conformal field theory of interest, which explains its earlier numerical observation in the literature.

In the context of the quest for a holographic formulation of quantum gravity, we investigate the basic boundary theory structure for loop quantum gravity. In 3+1 space-time dimensions, the boundary theory lives on the 2+1-dimensional time-like boundary and is supposed to describe the time evolution of the edge modes living on the 2-dimensional boundary of space, i.e. the space-time corner. Focusing on "electric" excitations -- quanta of area -- living on the corner, we formulate their dynamics in terms of classical spinor variables and we show that the coupling constants of a polynomial Hamiltonian can be understood as the components of a background boundary 2+1-metric. This leads to a deeper conjecture of a correspondence between boundary Hamiltonian and boundary metric states. We further show that one can reformulate the quanta of area data in terms of a SL(2,C) connection, transporting the spinors on the boundary surface and whose SU(2) component would define "magnetic" excitations (tangential Ashtekar-Barbero connection), thereby opening the door to writing the loop quantum gravity boundary dynamics as a 2+1-dimensional SL(2,C) gauge theory.

In this review article, we first discuss a possible regularization of the big bang curvature singularity of the standard Friedmann cosmology, where the curvature singularity is replaced by a spacetime defect. We then consider the hypothesis that a new physics phase gave rise to this particular spacetime defect. Specifically, we set out on an explorative calculation using the IIB matrix model, which has been proposed as a particular formulation of nonperturbative superstring theory (M-theory).

We derive a generalized Knizhnik-Zamolodchikov equation for the correlation function of the intertwiners of the vector and the MacMahon representations of Ding-Iohara-Miki algebra. These intertwiners are cousins of the refined topological vertex which is regarded as the intertwining operator of the Fock representation. The shift of the spectral parameter of the intertwiners is generated by the operator which is constructed from the universalRmatrix. The solutions to the generalized KZ equation are factorized into the ratio of two point functions which are identified with generalizations of the Nekrasov factor for supersymmetric quiver gauge theories

Vasiliev system of higher-spin equations contains a free complex parameterη. Solving the generating system order by order one obtains physical vertices proportional to various powers ofηandη¯. Recentlyη2andη¯2vertices in the field equations for zero-form field were written in theZ-dominated form implying their spin-locality by virtue ofZ-dominance Lemma. Here we obtain explicitZ-independent spin-local form for the vertexΥηη?CCCfor its?CCC-ordered part where?andCdenote gauge one-form and field strength zero-form higher-spin fields valued in arbitrary associative algebra in which case the order of product factors in?CCCmatters.

We derive a manifestly duality-symmetric formulation of the action principle for conformal gravity linearized around Minkowski space-time. The analysis is performed in the Hamiltonian formulation, the fourth-order character of the equations of motion requiring the formal treatment of the three-dimensional metric perturbation and the extrinsic curvature as independent dynamical variables. The constraints are solved in terms of two symmetric potentials that are interpreted as a dual three-dimensional metric and a dual extrinsic curvature. The action principle can be written in terms of these four dynamical variables, duality acting as simultaneous rotations in the respective spaces spanned by the three-dimensional metrics and the extrinsic curvatures. A twisted self-duality formulation of the equations of motion is also provided.