We propose a new class of vector fields to construct a conserved charge in a general field theory whose energy momentum tensor is covariantly conserved. We show that there always exists such a vector field in a given field theory even without global
symmetry. We also argue that the conserved current constructed from the (asymptotically) time-like vector field can be identified with the entropy current of the system. As a piece of evidence we show that the conserved charge defined therefrom satisfies the first law of thermodynamics for an isotropic system with a suitable definition of temperature. We apply our formulation to several gravitational systems such as the expanding universe, Schwarzschild and BTZ black holes, and gravitational plane waves. We confirm the conservation of the proposed entropy density under any homogeneous and isotropic expansion of the universe, the precise reproduction of the Bekenstein-Hawking entropy incorporating the first law of thermodynamics, and the existence of gravitational plane wave carrying no charge, respectively. We also comment on the energy conservation during gravitational collapse in simple models.
We present a precise definition of a conserved quantity from an arbitrary covariantly conserved current available in a general curved spacetime with Killing vectors. This definition enables us to define energy and momentum for matter by the volume in
tegral. As a result we can compute charges of Schwarzschild and BTZ black holes by the volume integration of a delta function singularity. Employing the definition we also compute the total energy of a static compact star. It contains both the gravitational mass known as the Misner-Sharp mass in the Oppenheimer-Volkoff equation and the gravitational binding energy. We show that the gravitational binding energy has the negative contribution at maximum by 68% of the gravitational mass in the case of a constant density. We finally comment on a definition of generators associated with a vector field on a general curved manifold.
We take a first step towards a holographic description of a black hole by means of a flow equation. We consider a free theory of multiple scalar fields at finite temperature and study its holographic geometry defined through a free flow of the scalar
fields. We find that the holographic metric has the following properties: i) It is an asymptotic Anti-de Sitter (AdS) black brane metric with some unknown matter contribution. ii) It has no coordinate singularity and milder curvature singularity. iii) Its time component decays exponentially at a certain AdS radial slice. We find that the matter spreads all over the space, which we speculate to be due to thermal excitation of infinitely many massless higher spin fields. We conjecture that the above three are generic features of a black hole holographically realized by the flow equation method.
The Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. The mathematical set-up for this theorem is, however, not directly related to the physical fermion system, as
it imposes on the fermion fields a non-local boundary condition known as the APS boundary condition by hand, which is unlikely to be realized in the materials. In this work, we attempt to reformulate the APS index in a physicist-friendly way for a simple set-up with $U(1)$ or $SU(N)$ gauge group on a flat four-dimensional Euclidean space. We find that the same index as APS is obtained from the domain-wall fermion Dirac operator with a local boundary condition, which is naturally given by the kink structure in the mass term. As the boundary condition does not depend on the gauge fields, our new definition of the index is easy to compute with the standard Fujikawa method.
We study the flow equation of the O($N$) $varphi^4$ model in $d$ dimensions at the next-to-leading order (NLO) in the $1/N$ expansion. Using the Schwinger-Dyson equation, we derive 2-pt and 4-pt functions of flowed fields. As the first application of
the NLO calculations, we study the running coupling defined from the connected 4-pt function of flowed fields in the $d+1$ dimensional theory. We show in particular that this running coupling has not only the UV fixed point but also an IR fixed point (Wilson-Fisher fixed point) in the 3 dimensional massless scalar theory. As the second application, we calculate the NLO correction to the induced metric in $d+1$ dimensions with $d=3$ in the massless limit. While the induced metric describes a 4-dimensional Euclidean Anti-de-Sitter (AdS) space at the leading order as shown in the previous paper, the NLO corrections make the space asymptotically AdS only in UV and IR limits. Remarkably, while the AdS radius does not receive a NLO correction in the UV limit, the AdS radius decreases at the NLO in the IR limit, which corresponds to the Wilson-Fisher fixed point in the original scalar model in 3 dimensions.
We propose a novel lattice calculation of spontaneous chiral symmetry breaking in QED model with 2+1 dimensional fermion brane. Considering the relativistic action with gauge symmetry we rigorously carry out path integral in Monte-Carlo simulation wi
th Fermi-velocity relevant to effective coupling constant. We numerically show the evidence of spontaneous chiral symmetry breaking in strong coupling region with chiral condensate, low-lying mode distribution and Nambu-Goldstone boson spectrum in bare Fermi-velocty $v=0.1$. This is a feasible study to investigate the phase structure of Graphene.
We study the flavor structure in the three site Higgsless model. In this model, the gauge bosons and fermions have heavy partners, coming from the Kaluza-Klein excitation in the dimensional deconstruction picture. The yukawa couplings are introduced
in a way to minimize the flavor chaning neutral current in the light sector at the tree level. Due to the flavor mixing between the light and the heavy partner fields, new effects on FCNCs appear at one-loop level. As an example of such FCNC processes, we calculate the contribution to the b -> s gamma amplitude in the three site Higgsless model. Interestingly, heavy particles which exist in the three site Higgsless model do not completely decouple in the heavy-mass limit. One-loop level b -> s gamma amplitude is calculated by considering all possible combinations of particles in the loop, then it is compared to the experiment. The result shows that the central value of the B -> X_s gamma branching ratio in the three site Higgsless model takes closer value to its experimental central value as one takes the larger value of a free parameter, varepsilon_{tR}, within a range allowed by the precision electroweak measurement.
Lattice quantum chromodynamics provides first principles calculations for hadrons containing heavy quarks -- charm and bottom quarks. Their mass spectra, decay rates, and some hadronic matrix elements can be calculated on the lattice in a model indep
endent manner. In this review, we introduce the effective theories that treat heavy quarks on the lattice. We summarize results on the heavy quarkonium spectrum, which verify the validity of the effective theory approach. We then discuss applications to $B$ physics, which is the main target of the lattice theory of heavy quarks. We review progress in lattice calculations of the $B$ meson decay constant, the $B$ parameter, semi-leptonic decay form factors, and other important quantities.)
