Winnipeg Institute for Theoretical Physics

We compute leading order corrections to the the entropy of any thermodynamic system due to small statistical fluctuations around equilibrium. When applied to black holes, these corrections are shown to be of the form $-k\\ln(Area)$. For BTZ black holes, $k=3/2$, as found earlier. We extend the result to anti-de Sitter Schwarzschild and Reissner-Nordstrom black holes in arbitrary dimensions. Finally we examine the role of conformal field theory in black hole entropy and its corrections.

Starting from recent observations about quasinormal modes, we use semiclassical arguments to derive the Bekenstein-Hawking entropy spectrum for $d$-dimensional spherically symmetric black holes. We find that, as first suggested by Bekenstein, the entropy spectrum is equally spaced: ${S}_{\mathrm{B}\mathrm{H}}=k\mathrm{ln}({m}_{0})n$, where ${m}_{0}$ is a fixed integer that must be derived from the microscopic theory. As shown in O. Dreyer, gr-qc/0211076, 4D loop quantum gravity yields precisely such a spectrum with ${m}_{0}=3$ providing the Immirzi parameter is chosen appropriately. For $d$-dimensional black holes of radius ${R}_{H}(M)$, our analysis predicts the existence of a unique quasinormal mode frequency in the large damping limit ${\ensuremath{\omega}}^{(d)}(M)={\ensuremath{\alpha}}^{(d)}c/{R}_{H}(M)$ with coefficient ${\ensuremath{\alpha}}^{(d)}=\frac{(d\ensuremath{-}3)}{4\ensuremath{\pi}}\mathrm{ln}({m}_{0})$, where ${m}_{0}$ is an integer.

Following an earlier suggestion of the authors(gr-qc/9607030), we use some basic properties of Euclidean black hole thermodynamics and the quantum mechanics of systems with periodic phase space coordinate to derive the discrete two-parameter area spectrum of generic charged spherically symmetric black holes in any dimension. For the Reissner-Nordstrom black hole we get $A/4G\\hbar=\\pi(2n+p+1)$, where the integer p=0,1,2,.. gives the charge spectrum, with $Q=\\pm\\sqrt{\\hbar p}$. The quantity $\\pi(2n+1)$, n=0,1,... gives a measure of the excess of the mass/energy over the critical minimum (i.e. extremal) value allowed for a given fixed charge Q. The classical critical bound cannot be saturated due to vacuum fluctuations of the horizon, so that generically extremal black holes do not appear in the physical spectrum. Consistency also requires the black hole charge to be an integer multiple of any fundamental elementary particle charge: Q=me, m=0,1,2,.... As a by-product this yields a relation between the fine structure constant and integer parameters of the black hole -- a kind of the Coleman big fix mechanism induced by black holes. In four dimensions, this relationship is $e^2/\\hbar=p/m^2$ and requires the fine structure constant to be a rational number. Finally, we prove that the horizon area is an adiabatic invariant, as has been conjectured previously.

We quantize the spherically symmetric sector of generic charged black holes. Thermal properties are incorporated by imposing periodicity in Euclidean time, with period equal to the inverse Hawking temperature of the black hole. This leads to an exact quantization of the area (A) and charge (Q) operators. For the Reissner–Nordström black hole, A=4πGℏ(2n+p+1) and Q=me, for integers n,p,m. Consistency requires the fine structure constant to be quantized: e2/ℏ=p/m2. Remarkably, vacuum fluctuations exclude extremal black holes from the spectrum, while near extremal black holes are highly quantum objects. We also prove that horizon area is an adiabatic invariant.

The most general dilaton gravity theory in two spacetime dimensions is studied. It is proven that, up to spacetime diffeomorphisms, the general solutions of the field equations form a one-parameter family of distinct static solutions. It is explained how this result is consistent with a recent analysis showing that the reduced phase space for this class of theories is two dimensional. In particular, the second phase space degree of freedom is explicitly constructed in terms of spacetime diffeomorphisms that cannot be generated canonically by local gauge transformations.

Pure $SU(3)$ glue theories exhibit a deconfining phase transition at a nonzero temperature, ${T}_{c}$. Using lattice measurements of the pressure, we develop a simple matrix model to describe the transition region, when $T\ensuremath{\ge}{T}_{c}$. This model, which involves three parameters, is used to compute the behavior of the 't Hooft loop. There is a Higgs phase in this region, where off-diagonal color modes are heavy, and diagonal modes are light. Lattice measurements of the latter suggest that the transition region is narrow, extending only to about $\ensuremath{\sim}1.2{T}_{c}$. This is in stark contrast to lattice measurements of the renormalized Polyakov loop, which indicates a much wider width. The possible implications for the differences in heavy ion collisions between the Relativistic Heavy Ion Collider and the LHC are discussed.

In this paper, we derive a simple sum rule satisfied by the gluon spectral function at finite temperature. This sum rule is useful in order to calculate exactly some integrals that appear frequently in the photon or dilepton production rate by a quark gluon plasma. Using this sum rule, we rederive simply some known results and obtain some new results that would be extremely difficult to justify otherwise. In particular, we derive an exact expression for the collision integral that appears in the calculation of the Landau-Pomeranchuk-Migdal effect.

We recast the tools of ``global causal analysis'' in accord with an approach to the subject animated by two distinctive features: a thoroughgoing reliance on order-theoretic concepts, and a utilization of the Vietoris topology for the space of closed subsets of a compact set. We are led to work with a new causal relation which we call $K^+$, and in terms of it we formulate extended definitions of concepts like causal curve and global hyperbolicity. In particular we prove that, in a spacetime $\M$ which is free of causal cycles, one may define a causal curve simply as a compact connected subset of $\M$ which is linearly ordered by $K^+$. Our definitions all make sense for arbitrary $C^0$ metrics (and even for certain metrics which fail to be invertible in places). Using this feature, we prove for a general $C^0$ metric, the familiar theorem that the space of causal curves between any two compact subsets of a globally hyperbolic spacetime is compact. We feel that our approach, in addition to yielding a more general theorem, simplifies and clarifies the reasoning involved. Our results have application in a recent positive energy theorem, and may also prove useful in the study of topology change. We have tried to make our treatment self-contained by including proofs of all the facts we use which are not widely available in reference works on topology and differential geometry.

We consider one-loop quantum corrections to the thermodynamics of a black hole in generic two-dimensional dilaton gravity. The classical action is the most general diffeomorphism invariant action in 1+1 space-time dimensions that contains a metric, dilaton, and Abelian gauge field, and having at most second derivatives of the fields. Quantum corrections are introduced by considering the effect of matter fields conformally coupled to the metric and nonminimally coupled to the dilaton. Back reaction of the matter fields (via nonvanishing trace conformal anomaly) leads to quantum corrections to the black hole geometry. Quantum corrections also lead to modifications in the gravitational action and hence in expressions for thermodynamic quantities. One-loop corrections to both geometry and thermodynamics (energy, entropy) are calculated for the generic theory. The formalism is then applied to a charged black hole in spherically symmetric gravity and to a rotating Ba\~nados-Teitelboim-Zanelli black hole.

We consider the one-loop corrected geometry and thermodynamics of a rotating BTZ black hole by way of a dimensionally reduced dilaton model. The analysis begins with a comprehensive study of the non-extremal solution after which two different methods are invoked to study the extremal case. The first approach considers the extremal limit of the non-extremal calculations, whereas the second treatment is based on the following conjecture: extremal and non-extremal black holes are qualitatively distinct entities. We show that only the latter method yields regularity and consistency at the one-loop level. This is suggestive of a generalized third law of thermodynamics that forbids continuous evolution from non-extremal to extremal black hole geometries.

We consider transformations of the 2\ifmmode\times\else\texttimes\fi{}2 propagator matrix in real-time finite-temperature field theory, resulting in transformed n-point functions. As special cases of such a transformation we examine the Keldysh basis, the retarded/advanced RA basis, and a Feynman-like FF\ifmmode\bar\else\textasciimacron\fi{} basis, which differ in this context as to how ``economically'' certain constraints on the original propagator matrix elements are implemented. We also obtain the relation between some of these real-time functions and certain analytic continuations of the imaginary-time functions. Finally, we compare some aspects of these bases which arise in practical calculations.

We investigate the perturbative ambiguity of the radiatively induced Chern-Simons term in differential regularization. The result obtained by this method contains all those obtained by other regularization schemes and the ambiguity is explicitly characterized by an indefinite ratio of two renormalization scales. It is argued that the ambiguity can only be eliminated by either imposing a physical requirement or resorting to a more fundamental principle. Some calculation techniques in coordinate space are developed in the appendixes.

The damping rate to order ${g}^{2}T$ for fermions in the long-wavelength limit of hot gauge theories is calculated using the recently developed resummation methods in terms of hard thermal loops. Both a heavy and a massless fermion are considered. Ward identities between the effective propagators and vertices are used to formally prove the gauge independence of the damping rate to this order in a wide class of gauges.

We show that by a suitable choice of a time-dependent Hamiltonian, Deutsch's algorithm can be implemented by an adiabatic quantum computer. We extend our analysis to the Deutsch-Jozsa problem and estimate the required running time for both global and local adiabatic evolutions.

We investigate the precisely measured anomalous magnetic moment and Lamb shift as tests for the possible existence of radiatively induced Lorentz and $\mathrm{CPT}$ violation effects in quantum electrodynamics. To this end we calculate the one-loop vacuum polarization tensor and vertex radiative correction in the dimensional reduction and on-shell renormalization schemes. We explicitly show how the Lorentz and $\mathrm{CPT}$ violation sector affects the anomalous magnetic moment and Lamb shift. Remarkably, we find infrared divergences coming from Lorentz and $\mathrm{CPT}$ violating terms that do not cancel in physical cross sections. This result appears to place stringent constraints on the type of Lorentz or $\mathrm{CPT}$ violating terms that can be added to the QED Lagrangian.

We propose an economical model to explain the apparent 130 GeV gamma ray peak, found in the Fermi/LAT data, in terms of dark matter (DM) annihilation through a dipole moment interaction. The annihilating dark matter particles represent a subdominant component, with mass density 7--17% of the total DM density; and they only annihilate into $\ensuremath{\gamma}\ensuremath{\gamma}$, $\ensuremath{\gamma}Z$, and $ZZ$, through a magnetic (or electric) dipole moment. Annihilation into other standard model particles is suppressed, due to a DM mass splitting in the magnetic dipole case, or to $p$-wave scattering in the electric dipole case. In either case, the observed signal requires a dipole moment of strength $\ensuremath{\mu}\ensuremath{\sim}2/\mathrm{TeV}$. We argue that composite models are the preferred means of generating such a large dipole moment, and that the magnetic case is more natural than the electric one. We present a simple model involving a scalar and fermionic techniquark of a confining SU(2) gauge symmetry. We point out some generic challenges for getting such a model to work. The new physics leading to a sufficiently large dipole moment is below the TeV scale, indicating that the magnetic moment is not a valid effective operator for LHC physics, and that production of the strongly interacting constituents, followed by techni-hadronization, is a more likely signature than monophoton events. In particular, four-photon events from the decays of bound state pairs are predicted.

A multichannel algebraic scattering theory, to find solutions of coupled-channel scattering problems with interactions determined by collective models, has been structured to ensure that the Pauli principle is not violated. By tracking the results in the zero coupling limit, a correct interpretation of the subthreshold and resonant spectra of the compound system can be made. As an example, the neutron-12C system is studied defining properties of 13C to 10 MeV excitation. Accounting for the Pauli principle in collective coupled-channels models is crucial to the outcome.

We consider a symmetric scalar theory with quartic coupling in 4 dimensions and compare the standard 2PI calculation with a modified version which uses an exact renormalization group method. The set of integral differential equations that is obtained from the exact renormalization group method truncates naturally, without the introduction of additional approximations. The results of the two methods agree well, which shows that the exact renormalization group can be used at the level of the 2PI effective action to obtain finite results without the use of counterterms. The method therefore offers a promising starting point to study the renormalization of higher order $n$PI theories.

Properties of particle-unstable nuclei lying beyond the proton drip line can be ascertained by considering the (usually known) properties of its mirror neutron-rich system. We have used a multichannel algebraic scattering theory to map the known properties of the neutron-14C system to those of the proton-14O one from which we deduce that the particle-unstable 15F will have a spectrum of two low-lying broad resonances of positive parity and, at higher excitation, three narrow negative-parity ones. A key feature is to use coupling to Pauli-hindered states in the target.

We show that a semiclassical polymerization of the interior of Schwarzschild black holes gives rise to a tantalizing candidate for a nonsingular, single-horizon black hole spacetime. The exterior has nonzero quantum stress energy but closely approximates the classical spacetime for macroscopic black holes. The interior exhibits a bounce at a microscopic scale and then expands indefinitely to a Kantowski-Sachs spacetime. Polymerization therefore removes the singularity and produces a scenario reminiscent of past proposals for universe creation via quantum effects inside a black hole.