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Brian P. Dolan

Publications and source records attributed to Brian P. Dolan.

At least 37 records · Page 2Linked to original sources
arXiv2013

The compressibility of rotating black holes in D-dimensions

Treating the cosmological constant as a pressure, in the context of black hole thermodynamics, a thermodynamic volume for the black hole can be defined as being the thermodynamic variable conjugate to the pressure, in the sense of a Legendre transform. The thermodynamic volume is explicitly calculated, as the Legendre transform of the pressure in the enthalpy for a rotating asymptotically anti-de Sitter Myers-Perry black hole in D space-time dimensions. The volume obtained is shown to agree with previous calculations using the Smarr relation. The compressibility is calculated and shown to be non-negative and bounded. Taking the limit of zero cosmological constant, the compressibility of a rotating black hole in asymptotically flat space-times is determined and the corresponding speed of sound computed. The latter is bounded above and has an elegant expression purely in terms of the angular momenta, in the form of quartic and quadratic Casimirs of the rotation group, SO(D-1).

gr-qc↗
arXiv2013

Critical Behaviour of the Fuzzy Sphere

We study a multi-matrix model whose low temperature phase is a fuzzy sphere that undergoes an evaporation transition as the temperature is increased. We investigate finite size scaling of the system as the limiting temperature of stability of the fuzzy sphere phase is approached. We find on theoretical grounds that the system should obey scaling with specific heat exponent α=1/2, shift exponent \bar λ=4/3 and that the peak in the specific heat grows with exponent \bar ω=2/3. Using hybrid Monte Carlo simulations we find good collapse of specific heat data consistent with a scaling ansatz which give our best estimates for the scaling exponents as α=0.50 \pm 0.01,\bar λ=1.41 \pm 0.08 and \bar ω=0.66 \pm 0.08 .

hep-th↗
arXiv2013

Solitons and Yukawa Couplings in Nearly Kahler Flux Compactifications

We study vacuum states and symmetric fermions in equivariant dimensional reduction of Yang-Mills-Dirac theory over the six-dimensional homogeneous space SU(3)/U(1)x U(1) endowed with a family of SU(3)-structures including a nearly Kahler structure. We derive the fixed tree-level scalar potentials of the induced Yang-Mills-Higgs theory, and compute the dynamically generated gauge and Higgs boson masses as functions of the metric moduli of the coset space. We find an integrable subsector of the Higgs field theory which is governed by a sine-Gordon type model whose topological soliton solutions are determined nonperturbatively by the gauge coupling and which tunnel between families of infinitely degenerate vacua. The reduction of the Dirac action for symmetric fermions yields exactly massless chiral fermions, containing subsectors which have fixed tree-level Yukawa interactions. We compute dynamical fermion mass matrices explicitly and compare them at differents points of the moduli space, some of which support consistent heterotic flux vacua.

hep-th↗
arXiv2013

Thermodynamic Volumes and Isoperimetric Inequalities for de Sitter Black Holes

We consider the thermodynamics of rotating and charged asymptotically de Sitter black holes. Using Hamiltonian perturbation theory techniques, we derive three different first law relations including variations in the cosmological constant, and associated Smarr formulas that are satisfied by such spacetimes. Each first law introduces a different thermodynamic volume conjugate to the cosmological constant. We examine the relation between these thermodynamic volumes and associated geometric volumes in a number of examples, including Kerr-dS black holes in all dimensions and Kerr-Newman-dS black holes in D=4. We also show that the Chong-Cvetic-Lu-Pope solution of D=5 minimal supergravity, analytically continued to positive cosmological constant, describes black hole solutions of the Einstein-Chern-Simons theory and include such charged asymptotically de Sitter black holes in our analysis. In all these examples we find that the particular thermodynamic volume associated with the region between the black hole and cosmological horizons is equal to the naive geometric volume. Isoperimetric inequalities, which hold in the examples considered, are formulated for the different thermodynamic volumes and conjectured to remain valid for all asymptotically de Sitter black holes. In particular, in all examples considered, we find that for fixed volume of the observable universe, the entropy is increased by adding black holes. We conjecture that this is true in general.

hep-th↗
arXiv2013

AdS/QHE: Towards a Holographic Description of Quantum Hall Experiments

Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semi-circle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the DC ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero DC conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semi-circle transitions between them. The model can be regarded as a strongly coupled analog of the old `composite boson' picture of quantum Hall systems. Non-universal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model.

hep-th↗
arXiv2012

The cosmological constant and the black hole equation of state

The thermodynamics of black holes in various dimensions are described in the presence of a negative cosmological constant which is treated as a thermodynamic variable, interpreted as a pressure in the equation of state. The black hole mass is then identified with the enthalpy, rather than the internal energy, and heat capacities are calculated at constant pressure not at constant volume. The Euclidean action is associated with a bridge equation for the Gibbs free energy and not the Helmholtz free energy. Quantum corrections to the enthalpy and the equation of state of the BTZ black hole are studied.

gr-qc↗
arXiv2012

Scalar and Spinor Field Actions on Fuzzy $S^4$: fuzzy $CP^3$ as a $S^2_F$ bundle over $S^4_F$

We present a manifestly Spin(5) invariant construction of squashed fuzzy $CP^3$ as a fuzzy $S^2$ bundle over fuzzy $S^4$. We develop the necessary projectors and exhibit the squashing in terms of the radii of the $S^2$ and $S^4$. Our analysis allows us give both scalar and spinor fuzzy action functionals whose low lying modes are truncated versions of those of a commutative $S^4$.

hep-th↗
arXiv2011

Compressibility of rotating black holes

Interpreting the cosmological constant as a pressure, whose thermodynamically conjugate variable is a volume, modifies the first law of black hole thermodynamics. Properties of the resulting thermodynamic volume are investigated: the compressibility and the speed of sound of the black hole are derived in the case of non-positive cosmological constant. The adiabatic compressibility vanishes for a non-rotating black hole and is maximal in the extremal case --- comparable with, but still less than, that of a cold neutron star. A speed of sound $v_s$ is associated with the adiabatic compressibility, which is is equal to $c$ for a non-rotating black hole and decreases as the angular momentum is increased. An extremal black hole has $v_s^2=0.9 \,c^2$ when the cosmological constant vanishes, and more generally $v_s$ is bounded below by $c/ {\sqrt 2}$.

gr-qc↗
arXiv2011

Pressure and volume in the first law of black hole thermodynamics

The mass of a black hole is interpreted, in terms of thermodynamic potentials, as being the enthalpy, with the pressure given by the cosmological constant. The volume is then defined as being the Legendre transform of the pressure and the resulting relation between volume and pressure is explored in the case of positive pressure. A virial expansion is developed and a van der Waals like critical point determined. The first law of black hole thermodynamics includes a PdV term which modifies the maximal efficiency of a Penrose process. It is shown that, in four dimensional space-time with a negative cosmological constant an extremal charged rotating black hole can have an efficiency of up to 75%, while for an electrically neutral rotating back hole this figure is reduced to 52%, compared to the corresponding values of 50% and 29% respectively when the cosmological constant is zero.

gr-qc↗
arXiv2011

Dimensional Reduction and Vacuum Structure of Quiver Gauge Theory

We describe the structure of the vacuum states of quiver gauge theories obtained via dimensional reduction over homogeneous spaces, in the explicit example of SU(3)-equivariant dimensional reduction of Yang-Mills-Dirac theory on manifolds of the form M x CP(2). We pay particular attention to the role of topology of background gauge fields on the internal coset spaces, in this case U(1) magnetic monopoles and SU(2) instantons on CP(2). The reduction of Yang-Mills theory induces a quiver gauge theory involving coupled Yang-Mills-Higgs systems on M with a Higgs potential leading to dynamical symmetry breaking. The criterion for a ground state of the Higgs potential can be written as the vanishing of a non-abelian Yang-Mills flux on the quiver diagram, regarded as a lattice with group elements attached to the links. The reduction of SU(3)-symmetric fermions yields Dirac fermions on M transforming under the low-energy gauge group with Yukawa couplings. The fermionic zero modes on CP(2) yield exactly massless chiral fermions on M, though there is a unique choice of spin(c) structure on CP(2) for which some of the zero modes can acquire masses through Yukawa interactions. We work out the spontaneous symmetry breaking patterns and determine the complete physical particle spectrum in a number of explicit examples, some of which possess quantum number assignments qualitatively analogous to the manner in which vector bosons, quarks and leptons acquire masses in the standard model.

hep-th↗
arXiv2010

Holomorphic and anti-holomorphic conductivity flows in the quantum Hall effect

It is shown that the flow diagrams for the conductivities in the quantum Hall effect, arising from two ostensibly very different proposals based on modular symmetry, are in fact identical. The beta-functions are different, the rate at which the flow lines are traversed are different, but the tangents to the flow lines are the same in both cases, hence the flow diagrams are same in all aspects.

cond-mat.str-el↗
arXiv2010

Modular symmetry and temperature flow of conductivities in quantum Hall systems with varying Zeeman energy

The behaviour of the critical point between quantum Hall plateaux, as the Zeeman energy is varied, is analysed using modular symmetry of the Hall conductivities following from the law of corresponding states. Flow diagrams for the conductivities as a function of temperature, with the magnetic field fixed, are constructed for different Zeeman energies, for samples with particle-hole symmetry.

cond-mat.str-el↗
arXiv2010

Chiral fermions and torsion in the early Universe

Torsion arising from fermionic matter in the Einstein-Cartan formulation of general relativity is considered in the context of Robertson-Walker geometries and the early Universe. An ambiguity in the way torsion arising from hot fermionic matter in chiral models should be implemented is highlighted and discussed. In one interpretation, chemical potentials in chiral models can contribute to the Friedmann equation and give a negative contribution to the energy density.

gr-qc↗
arXiv2009

Dimensional Reduction, Monopoles and Dynamical Symmetry Breaking

We consider SU(2)-equivariant dimensional reduction of Yang-Mills-Dirac theory on manifolds of the form M x CP(1), with emphasis on the effects of non-trivial magnetic flux on CP(1). The reduction of Yang-Mills fields gives a chain of coupled Yang-Mills-Higgs systems on M with a Higgs potential leading to dynamical symmetry breaking, as a consequence of the monopole fields. The reduction of SU(2)-symmetric fermions gives massless Dirac fermions on M transforming under the low-energy gauge group with Yukawa couplings, again as a result of the internal U(1) fluxes. The tower of massive fermionic Kaluza-Klein states also has Yukawa interactions and admits a natural SU(2)-equivariant truncation by replacing CP(1) with a fuzzy sphere. In this approach it is possible to obtain exactly massless chiral fermions in the effective field theory with Yukawa interactions, without any further requirements. We work out the spontaneous symmetry breaking patterns and determine the complete physical particle spectrum in a number of explicit examples.

hep-th↗
arXiv2008

Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives

We generalise the construction of fuzzy CP^N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S^2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space.

hep-th↗
arXiv2007

Modular Symmetry and Fractional Charges in N=2 Supersymmetric Yang-Mills and the Quantum Hall Effect

The parallel roles of modular symmetry in ${\cal N}=2$ supersymmetric Yang-Mills and in the quantum Hall effect are reviewed. In supersymmetric Yang-Mills theories modular symmetry emerges as a version of Dirac's electric -- magnetic duality. It has significant consequences for the vacuum structure of these theories, leading to a fractal vacuum which has an infinite hierarchy of related phases. In the case of ${\cal N}=2$ supersymmetric Yang-Mills in 3+1 dimensions, scaling functions can be defined which are modular forms of a subgroup of the full modular group and which interpolate between vacua. Infra-red fixed points at strong coupling correspond to $θ$-vacua with $θ$ a rational number that, in the case of pure SUSY Yang-Mills, has odd denominator. There is a mass gap for electrically charged particles which can carry fractional electric charge. A similar structure applies to the 2+1 dimensional quantum Hall effect where the hierarchy of Hall plateaux can be understood in terms of an action of the modular group and the stability of Hall plateaux is due to the fact that odd denominator Hall conductivities are attractive infra-red fixed points. There is a mass gap for electrically charged excitations which, in the case of the fractional quantum Hall effect, carry fractional electric charge.

hep-th↗