234 research outputs found
Betti numbers for numerical semigroup rings
We survey results related to the magnitude of the Betti numbers of numerical
semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra
and Applications (V. Ene, E. Miller Eds.
Anomalies in Superfluids and a Chiral Electric Effect
We analyze the chiral transport terms in relativistic superfluid
hydrodynamics. In addition to the spontaneously broken symmetry current, we
consider an arbitrary number of unbroken symmetries and extend the results of
arXiv:1105.3733. We suggest an interpretation of some of the new transport
coefficients in terms of chiral and gravitational anomalies. In particular, we
show that with unbroken gauged charges in the system, one can observe a chiral
electric conductivity - a current in a perpendicular direction to the applied
electric field. We present a motivated proposal for the value of the associated
transport coefficient, linking it to the triangle anomaly. Along the way we
present new arguments regarding the interpretation of the anomalous transport
coefficients in normal fluids. We propose a natural generalization of the
chiral transport terms to the case of an arbitrary number of spontaneously
broken symmetry currents.Comment: 30 pages; v2: Onsager-relations argument corrected, references added;
v3: fixed missing line in eq. (38
Regularity of Edge Ideals and Their Powers
We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals
of graphs and their powers. Our focus is on bounds and exact values of and the asymptotic linear function , for in terms of combinatorial data of the given graph Comment: 31 pages, 15 figure
The R*-operation for Feynman graphs with generic numerators
Abstract The R *-operation by Chetyrkin, Tkachov, and Smirnov is a generalisation of the BPHZ R-operation, which subtracts both ultraviolet and infrared divergences of euclidean Feynman graphs with non-exceptional external momenta. It can be used to compute the divergent parts of such Feynman graphs from products of simpler Feynman graphs of lower loops. In this paper we extend the R *-operation to Feynman graphs with arbitrary numerators, including tensors. We also provide a novel way of defining infrared counterterms which closely resembles the definition of its ultraviolet counterpart. We further express both infrared and ultraviolet counterterms in terms of scaleless vacuum graphs with a logarithmic degree of divergence. By exploiting symmetries, integrand and integral relations, which the counterterms of scaleless vacuum graphs satisfy, we can vastly reduce their number and complexity. A FORM implementation of this method was used to compute the five loop beta function in QCD for a general gauge group. To illustrate the procedure, we compute the poles in the dimensional regulator of all top-level propagator graphs at five loops in four dimensional Ï 3 theory
Geometric IR subtraction for final state real radiation
A scheme is proposed for the subtraction of soft and collinear divergences
present in massless real emission phase space integrals. The scheme is based on
a local slicing procedure which utilises the soft and collinear factorisation
properties of amplitudes to produce universal counter-terms whose analytic
integration is relatively simple. We propose that this scheme can be promoted
to a fully local subtraction method. As a first application the scheme is
applied to establish a general pole formula for final state real radiation at
NLO and NNLO in Yang Mills theory for arbitrary multiplicities. All required
counter-terms are evaluated to all orders in the dimensional regulator in terms
of - and hypergeometric - functions. As a proof of principle
the poles in the dimensional regulator of the double real emission
contribution to the decay rate are reproduced.Comment: 48 pages, 7 figure
Quantum magnetism and criticality
Magnetic insulators have proved to be fertile ground for studying new types
of quantum many body states, and I survey recent experimental and theoretical
examples. The insights and methods transfer also to novel superconducting and
metallic states. Of particular interest are critical quantum states, sometimes
found at quantum phase transitions, which have gapless excitations with no
particle- or wave-like interpretation, and control a significant portion of the
finite temperature phase diagram. Remarkably, their theory is connected to
holographic descriptions of Hawking radiation from black holes.Comment: 39 pages, 10 figures, review article for non-specialists; (v2) added
clarifications and references; (v3) minor corrections; (v4) added footnote on
hydrodynamic long-time tail
Chiral drag force
We provide a holographic evaluation of novel contributions to the drag force
acting on a heavy quark moving through strongly interacting plasma. The new
contributions are chiral in that they act in opposite directions in plasmas
containing an excess of left- or right-handed quarks and in that they are
proportional to the coefficient of the axial anomaly. These new contributions
to the drag force act either parallel to or antiparallel to an external
magnetic field or to the vorticity of the fluid plasma. In all these respects,
these contributions to the drag force felt by a heavy quark are analogous to
the chiral magnetic effect on light quarks. However, the new contribution to
the drag force is independent of the electric charge of the heavy quark and is
the same for heavy quarks and antiquarks. We show that although the chiral drag
force can be non-vanishing for heavy quarks that are at rest in the local fluid
rest frame, it does vanish for heavy quarks that are at rest in a suitably
chosen frame. In this frame, the heavy quark at rest sees counterpropagating
momentum and charge currents, both proportional to the axial anomaly
coefficient, but feels no drag force. This provides strong concrete evidence
for the absence of dissipation in chiral transport, something that has been
predicted previously via consideration of symmetries. Along the way to our
principal results, we provide a general calculation of the corrections to the
drag force due to the presence of gradients in the flowing fluid in the
presence of a nonzero chemical potential. We close with a consequence of our
result that is at least in principle observable in heavy ion collisions, namely
an anticorrelation between the direction of the CME current for light quarks in
a given event and the direction of the kick given to the momentum of all the
heavy quarks and antiquarks in that event.Comment: 28 pages, small improvement to the discussion of gravitational
anomaly, references adde
Field theories with anisotropic scaling in 2D, solitons and the microscopic entropy of asymptotically Lifshitz black holes
Field theories with anisotropic scaling in 1+1 dimensions are considered. It
is shown that the isomorphism between Lifshitz algebras with dynamical
exponents z and 1/z naturally leads to a duality between low and high
temperature regimes. Assuming the existence of gap in the spectrum, this
duality allows to obtain a precise formula for the asymptotic growth of the
number of states with a fixed energy which depends on z and the energy of the
ground state, and reduces to the Cardy formula for z=1. The holographic
realization of the duality can be naturally inferred from the fact that
Euclidean Lifshitz spaces in three dimensions with dynamical exponents and
characteristic lengths given by z, l, and 1/z, l/z, respectively, are
diffeomorphic. The semiclassical entropy of black holes with Lifshitz
asymptotics can then be recovered from the generalization of Cardy formula,
where the ground state corresponds to a soliton. An explicit example is
provided by the existence of a purely gravitational soliton solution for BHT
massive gravity, which precisely has the required energy that reproduces the
entropy of the analytic asymptotically Lifshitz black hole with z=3.
Remarkably, neither the asymptotic symmetries nor central charges were
explicitly used in order to obtain these results.Comment: 17 pages, no figures, references corrected and update
Charged, conformal non-relativistic hydrodynamics
We embed a holographic model of an U(1) charged fluid with Galilean
invariance in string theory and calculate its specific heat capacity and
Prandtl number. Such theories are generated by a R-symmetry twist along a null
direction of a N=1 superconformal theory. We study the hydrodynamic properties
of such systems employing ideas from the fluid-gravity correspondence.Comment: 31 pages, 1 figure, JHEP3 style, refs added, typos corrected, missing
terms in spatial charge current and field corrections added, to be published
in JHE
F-Theorem without Supersymmetry
The conjectured F-theorem for three-dimensional field theories states that
the finite part of the free energy on S^3 decreases along RG trajectories and
is stationary at the fixed points. In previous work various successful tests of
this proposal were carried out for theories with {\cal N}=2 supersymmetry. In
this paper we perform more general tests that do not rely on supersymmetry. We
study perturbatively the RG flows produced by weakly relevant operators and
show that the free energy decreases monotonically. We also consider large N
field theories perturbed by relevant double trace operators, free massive field
theories, and some Chern-Simons gauge theories. In all cases the free energy in
the IR is smaller than in the UV, consistent with the F-theorem. We discuss
other odd-dimensional Euclidean theories on S^d and provide evidence that
(-1)^{(d-1)/2} \log |Z| decreases along RG flow; in the particular case d=1
this is the well-known g-theorem.Comment: 34 pages, 2 figures; v2 refs added, minor improvements; v3 refs
added, improved section 4.3; v4 minor improvement
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