High Energy Physics Theory

We revisit the proposal that the ensemble average over free boson CFTs in two dimensions - parameterized by Narain's moduli space - is dual to an exotic theory of gravity in three dimensions dubbedU(1)gravity. We consider flavored partition functions, where the usual genusgpartition function is weighted by Wilson lines coupled to the conservedU(1)currents of these theories. These flavored partition functions obey a heat equation which relates deformations of the Riemann surface moduli to those of the chemical potentials which measure theseU(1)charges. This allows us to derive a Siegel-Weil formula which computes the average of these flavored partition functions. The result takes the form of a "sum over geometries," albeit with modifications relative to the unflavored case.

There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planarN=4SYM. A long standing question has been precisely how algebraic branch points emerge from this picture. We use wall crossing and scattering diagrams to systematically study the boundary structure of the positive kinematic regions associated with MHV amplitudes. The notion of asymptotic chambers in the scattering diagram naturally explains the appearance of algebraic branch points. Furthermore, the scattering diagram construction also motivates a new coordinate system for kinematic space that rationalizes the relations between algebraic letters in the symbol alphabet. As a direct application, we conjecture a complete list of all algebraic letters that could appear in the symbol alphabet of the 8-point MHV amplitude.

The integrability-condition method is regarded as a mathematical tool to describe the symmetry of collective sub-manifold. We here adopt the particle-hole representation. In the conventional time-dependent (TD) self-consistent field (SCF) theory, we take the one-form linearly composed of the TD SCF Hamiltonian and the infinitesimal generator induced by the collective-variable differential of canonical transformation on a group. Standing on the differential geometrical viewpoint, we introduce a Lagrange-like manner familiar to fluid dynamics to describe collective coordinate systems. We construct a geometric equation, noticing the structure of coset space SU(m+n)/S(U(m) x U(n)). To develop a perturbative method with the use of the collective variables, we aim at constructing a new fermion SCF theory, i.e., renewal of TD Hartree-Fock (TDHF) theory by using the canonicity condition under the existence of invariant subspace in the whole HF space. This is due to a natural consequence of the maximally decoupled theory because there exists an invariant subspace, if the invariance principle of Schredinger equation is realized. The integrability condition of the TDHF equation determining a collective sub-manifold is studied, standing again on the differential geometric viewpoint. A geometric equation works well over a wide range of physics beyond the random phase approximation.

We review the construction of almost contact metric (three-) structures on manifolds with aG2structure. These are of interest for certain supersymmetric configurations in string and M-theory. We compute the torsion of the SU(3) structure associated to an ACMS and apply these computations to heteroticG2systems and supersymmetry enhancement. We initiate the study of the space of ACM3Ss, which is an infinite dimensional space with a local product structure and interesting topological features. Tantalising links between ACM3Ss and associative and coassociative submanifolds are observed.

Collective coordinates provide a powerful tool for separating collective and elementary excitations, allowing both to be treated in the full quantum theory. The price is a canonical transformation which leads to a complicated starting point for subsequent calculations. Sometimes the collective behavior of a soliton is simple but nontrivial, and one is interested in the elementary excitations. We show that in this case an alternative prescription suffices, in which the canonical transformation is not necessary. The use of a nonperturbative operator which creates a soliton state allows the theory to be constructed perturbatively in terms of the soliton normal modes. We show how translation invariance may be perturbatively imposed. We apply this to construct the two-loop ground state of an arbitrary scalar kink.

A general covariant local field theory of the holographic dark energy model is presented. It turns out the low energy effective theory of the holographic dark energy is the massive gravity theory whose graviton has 3 polarisations, including one scalar mode and two tensor modes. The Compton wavelength is the size of the future event horizon of the universe. The physical interpretation for the UV-IR correspondence???Mp/L????????????in the holographic dark energy model is provided in the framework of our effective field theory, whereLis interpreted as the graviton's Compton wavelength, and?is interpreted as the energy scale where the scalar graviton strongly couples to itself.

When a black hole first forms, the properties of the emitted radiation as measured by observers near future null infinity are very close to the 1974 prediction of Hawking. However, deviations grow with time, and become of order unity after a timet??M7/3i, whereMiis the initial mass in Planck units. After an evaporation time the corrections are large: the angular distribution of the emitted radiation is no longer dominated by low multipoles, with an exponential fall off at high multipoles. Instead, the radiation is redistributed as a power law spectrum over a broad range of angular scales, all the way down to the scale?θ??/Mi, beyond which there is exponential falloff. This effect is is a quantum gravitational effect, whose origin is the spreading of the wavefunction of the black hole's center of mass location caused by the kicks of the individual outgoing quanta, discovered by Page in 1980. The modified angular distribution of the Hawking radiation has an important consequence: the number of soft hair modes that can effectively interact with outgoing Hawking quanta increases from the handful of modes at low multipolesl, to a large number of modes, of order??M2i. We argue that this change unlocks the Hawking-Perry-Strominger mechanism for purifying the Hawking radiation.

We study an analog hydrodynamic model that mimics a 3+1 AdS planar BH spacetime dual to a 2+1-dimensional superconductor. We demonstrate that the AdS4bulk and its holographic dual could be realized in nature in an analog gravity model based on fluid dynamics. In particular we mimic the metric of anO2holographic superconductor and calculate the entanglement entropy of a conveniently designed subsystem at the boundary of the analog AdS4bulk.

We propose that Hawking radiation-like phenomena may be observed in systems that show butterfly effects. Suppose that a classical dynamical system has a Lyapunov exponentλL, and is deterministic and non-thermal (T=0). We argue that, if we quantize this system, the quantum fluctuations may imitate thermal fluctuations with temperatureT?��?λL/2?in a semi-classical regime, and it may cause analogous Hawking radiation. We also discuss that our proposal may provide an intuitive explanation of the existence of the bound of chaos proposed by Maldacena, Shenker and Stanford.

In this paper, we investigate the Dirac equation with the Killingbeck potential under the external magnetic field in non-commutative space. Corresponding to the expressions of the energy level and wave functions in spin symmetry limit and pseudo-spin symmetry limit are derived by using the Bethe ansatz method. The parameter B associated with the external magnetic field and non-commutative parameter {\theta} make to modify the energy level for considered systems.