281 research outputs found
A projective Dirac operator on CP^2 within fuzzy geometry
We propose an ansatz for the commutative canonical spin_c Dirac operator on
CP^2 in a global geometric approach using the right invariant (left action-)
induced vector fields from SU(3). This ansatz is suitable for noncommutative
generalisation within the framework of fuzzy geometry. Along the way we
identify the physical spinors and construct the canonical spin_c bundle in this
formulation. The chirality operator is also given in two equivalent forms.
Finally, using representation theory we obtain the eigenspinors and calculate
the full spectrum. We use an argument from the fuzzy complex projective space
CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show
that our commutative projected spin_c bundle has the correct
SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos
correcte
Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization
We investigate the critical behaviour of charged and rotating AdS black holes
in d spacetime dimensions, including effects from non-linear electrodynamics
via the Born-Infeld action, in an extended phase space in which the
cosmological constant is interpreted as thermodynamic pressure. For
Reissner-Nordstrom black holes we find that the analogy with the Van der Walls
liquid-gas system holds in any dimension greater than three, and that the
critical exponents coincide with those of the Van der Waals system. We find
that neutral slowly rotating black holes in four space-time dimensions also
have the same qualitative behaviour. However charged and rotating black holes
in three spacetime dimensions do not exhibit critical phenomena. For
Born-Infeld black holes we define a new thermodynamic quantity B conjugate to
the Born-Infeld parameter b that we call Born-Infeld vacuum polarization. We
demonstrate that this quantity is required for consistency of both the first
law of thermodynamics and the corresponding Smarr relation.Comment: 23 pages, 32 figures, v2: minor changes, upgraded reference
Matrix models on the fuzzy sphere
Field theory on a fuzzy noncommutative sphere can be considered as a
particular matrix approximation of field theory on the standard commutative
sphere. We investigate from this point of view the scalar theory. We
demonstrate that the UV/IR mixing problems of this theory are localized to the
tadpole diagrams and can be removed by an appropiate (fuzzy) normal ordering of
the vertex. The perturbative expansion of this theory reduces in the
commutative limit to that on the commutative sphere.Comment: 6 pages, LaTeX2e, Talk given at the NATO Advanced Research Workshop
on Confiment, Topology, and other Non-Perturbative Aspects of QCD, Stara
Lesna, Slovakia, Jan. 21-27, 200
A holographic model for the fractional quantum Hall effect
Experimental data for fractional quantum Hall systems can to a large extent
be explained by assuming the existence of a modular symmetry group commuting
with the renormalization group flow and hence mapping different phases of
two-dimensional electron gases into each other. Based on this insight, we
construct a phenomenological holographic model which captures many features of
the fractional quantum Hall effect. Using an SL(2,Z)-invariant
Einstein-Maxwell-axio-dilaton theory capturing the important modular
transformation properties of quantum Hall physics, we find dyonic diatonic
black hole solutions which are gapped and have a Hall conductivity equal to the
filling fraction, as expected for quantum Hall states. We also provide several
technical results on the general behavior of the gauge field fluctuations
around these dyonic dilatonic black hole solutions: We specify a sufficient
criterion for IR normalizability of the fluctuations, demonstrate the
preservation of the gap under the SL(2,Z) action, and prove that the
singularity of the fluctuation problem in the presence of a magnetic field is
an accessory singularity. We finish with a preliminary investigation of the
possible IR scaling solutions of our model and some speculations on how they
could be important for the observed universality of quantum Hall transitions.Comment: 86 pages, 16 figures; v.2 references added, typos fixed, improved
discussion of ref. [39]; v.3 more references added and typos fixed, several
statements clarified, v.4 version accepted for publication in JHE
P-V criticality of charged AdS black holes
Treating the cosmological constant as a thermodynamic pressure and its
conjugate quantity as a thermodynamic volume, we reconsider the critical
behaviour of charged AdS black holes. We complete the analogy of this system
with the liquid-gas system and study its critical point, which occurs at the
point of divergence of specific heat at constant pressure. We calculate the
critical exponents and show that they coincide with those of the Van der Waals
system.Comment: 13 pages, 15 figures, v2:added reference
Black hole thermodynamics with conical defects
Recently we have shown [1] how to formulate a thermodynamic first law for a single (charged) accelerated black hole in AdS space by fixing the conical deficit angles present in the spacetime. Here we show how to generalise this result, formulating thermodynamics for black holes with varying conical deficits. We derive a new potential for the varying tension defects: the thermodynamic length, both for accelerating and static black holes. We discuss possible physical processes in which the tension of a string ending on a black hole might vary, and also map out the thermodynamic phase space of accelerating black holes and explore their critical phenomena
Thermodynamic curvature and black holes
I give a relatively broad survey of thermodynamic curvature , one spanning
results in fluids and solids, spin systems, and black hole thermodynamics.
results from the thermodynamic information metric giving thermodynamic
fluctuations. has a unique status in thermodynamics as being a geometric
invariant, the same for any given thermodynamic state. In fluid and solid
systems, the sign of indicates the character of microscopic interactions,
repulsive or attractive. gives the average size of organized mesoscopic
fluctuating structures. The broad generality of thermodynamic principles might
lead one to believe the same for black hole thermodynamics. This paper explores
this issue with a systematic tabulation of results in a number of cases.Comment: 27 pages, 10 figures, 7 tables, 78 references. Talk presented at the
conference Breaking of Supersymmetry and Ultraviolet Divergences in extended
Supergravity, in Frascati, Italy, March 27, 2013. v2 corrects some small
problem
- …