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arXiv2011

Spherically Symmetric Solutions in Ghost-Free Massive Gravity

Recently, a class of theories of massive gravity has been shown to be ghost-free. We study the spherically symmetric solutions in the bigravity formulation of such theories. In general, the solutions admit both a Lorentz invariant and a Lorentz breaking asymptotically flat behaviour and also fall in two branches. In the first branch, all solutions can be found analitycally and are Schwarzschild-like, with no modification as is found for other classes of theories. In the second branch, exact solutions are hard to find, and relying on perturbation theory, Yukawa-like modifications of the static potential are found. The general structure of the solutions suggests that the bigravity formulation of massive gravity is crucial and more than a tool.

hep-th↗

arXiv2012

Casimir-Polder repulsion: Polarizable atoms, cylinders, spheres, and ellipsoids

Recently, the topic of Casimir repulsion has received a great deal of attention, largely because of the possibility of technological application. The general subject has a long history, going back to the self-repulsion of a conducting spherical shell and the repulsion between a perfect electric conductor and a perfect magnetic conductor. Recently it has been observed that repulsion can be achieved between ordinary conducting bodies, provided sufficient anisotropy is present. For example, an anisotropic polarizable atom can be repelled near an aperture in a conducting plate. Here we provide new examples of this effect, including the repulsion on such an atom moving on a trajectory nonintersecting a conducting cylinder; in contrast, such repulsion does not occur outside a sphere. Classically, repulsion does occur between a conducting ellipsoid placed in a uniform electric field and an electric dipole. The Casimir-Polder force between an anisotropic atom and an anisotropic dielectric semispace does not exhibit repulsion. The general systematics of repulsion are becoming clear.

hep-th↗

arXiv2011

Spin Non-commutativity and the Three-Dimensional Harmonic Oscillator

A three-dimensional harmonic oscillator with spin non-commutativity in the phase space is considered. The system has a regular symplectic structure and by using supersymmetric quantum mechanics techniques, the ground state is calculated exactly. We find that this state is infinitely degenerate and it has explicit spontaneous broken symmetry. Analyzing the Heisenberg equations, we show that the total angular momentum is conserved.

hep-th↗

arXiv2012

N=2 supersymmetric theories on squashed three-sphere

We investigate a squashing deformation of 3d N=2 supersymmetric theories on three-sphere, which have four supercharges. The deformation preserves SU(2)_L x U(1)_r isometry and all four supersymmetries. We compute the partition function and find non-trivial dependence on the squashing parameter. We also consider the large N limit of a certain class of quiver gauge theories which have free energy of order N^{3/2}, and show that the free energy on the squashed sphere differs from that on round sphere by a certain factor depending only on the squashing parameter.

hep-th↗

arXiv2011

Twinlike models with identical linear fluctuation spectra

Recently, the possibility of so-called twinlike field theories has been demonstrated, that is, of different field theories which share the same topological defect solution with the same energy density. Further, purely algebraic conditions have been derived which the corresponding Lagrangians have to obey in order that the field theories be twins of each other. A further diagnostical tool which, in general, allows to distinguish the topological defects of a given theory from the corresponding defects of its twins is the spectrum of linear fluctuations about these defects. Very recently, however, explicit examples of twin theories have been constructed such that not only their shapes and energy densities coincide, but also their linear fluctuation spectra are the same. Here we show that, again, there exist purely algebraic conditions for the Lagrangian densities which imply that the corresponding field theories are twins and that the fluctuation spectra about their defects coincide. These algebraic conditions allow to construct an infinite number of twins with coinciding fluctuation spectra for a given theory, and we provide some explicit examples. The importance of this result is related to the fact that coinciding defects with coinciding energy densities and identical fluctuation spectra are almost indistinguishable physically, that is, indistinguishable in a linear or semiclassical approximation. This implies that the measurable physical properties of a kink, in general, do not allow to determine the theory which provides the kink uniquely. Instead, in principle an infinite number of possible theories has to be considered.

hep-th↗

arXiv2012

Semiclassical correlators of three states with large S^5 charges in string theory in AdS_5 x S^5

We consider semiclassical computation of 3-point correlation functions of (BPS or non-BPS) string states represented by vertex operators carrying large charges in S5. We argue that the AdS5 part of the construction of relevant semiclassical solution involves the two basic ingredients: (i) configuration of three glued geodesics in AdS2 suggested by Klose and McLoughlin in arXiv:1106.0495 and (ii) a particular Schwarz-Christoffel map of the 3-geodesic solution in cylindrical (tau, sigma) domain into the complex plane with three marked points. This map is constructed using the expression for the AdS2 string stress tensor which is uniquely determined by the 3 scaling dimensions as noted by Janik and Wereszczynski in arXiv:1109.6262 (our solution, however, is different from theirs). We also find the S5 part of the solution and thus the full expression for the semiclassical part of the 3-point correlator for several examples: extremal and non-extremal correlators of BPS states and a particular correlator of "small" circular spinning strings in S3 part of S5. We demonstrate that for the BPS correlators the results agree with the large charge limit of the corresponding supergravity and free gauge theory expressions.

hep-th↗

arXiv2012

Transport coefficients of D1-D5-P system and the membrane paradigm

I discuss a correspondence between string theory and the black hole membrane paradigm in the context of the D1-D5-P system. By using the Kubo formula, I calculate transport coefficients of the effective string model induced by two kinds of minimal scalars. Then, I show that these transport coefficients exactly agree with the corresponding membrane transport coefficients of a five-dimensional near-extremal black hole with three charges.

hep-th↗

arXiv2011

${\cal N}=3$ Supersymmetric Effective Action of D2-branes in Massive IIA String Theory

We obtain a new-type of ${\cal N}=3$ Yang-Mills Chern-Simons theory from the Mukhi-Papageorgakis Higgsing of the ${\cal N}=3$ Gaiotto-Tomasiello theory. This theory has ${\cal N}=1$ BPS fuzzy funnel solution which is expressed in terms of the seven generators of SU(3), excluding $T_8$. We propose that this is an effective theory of multiple D2-branes with D6- and D8-branes background in massive IIA string theory.

hep-th↗

arXiv2012

Strings from Feynman Graph counting : without large N

A well-known connection between n strings winding around a circle and permutations of n objects plays a fundamental role in the string theory of large N two dimensional Yang Mills theory and elsewhere in topological and physical string theories. Basic questions in the enumeration of Feynman graphs can be expressed elegantly in terms of permutation groups. We show that these permutation techniques for Feynman graph enumeration, along with the Burnside counting lemma, lead to equalities between counting problems of Feynman graphs in scalar field theories and Quantum Electrodynamics with the counting of amplitudes in a string theory with torus or cylinder target space. This string theory arises in the large N expansion of two dimensional Yang Mills and is closely related to lattice gauge theory with S_n gauge group. We collect and extend results on generating functions for Feynman graph counting, which connect directly with the string picture. We propose that the connection between string combinatorics and permutations has implications for QFT-string dualities, beyond the framework of large N gauge theory.

hep-th↗

arXiv2012

Phase transition and monopole production in supergravity inflation

In F-term supergravity inflation models, scalar fields other than the inflaton generically receive a Hubble induced mass, which may restore gauge symmetries during inflation and phase transitions may occur during or after inflation as the Hubble parameter decreases. We study monopole (and domain wall) production associated with such a phase transition in chaotic inflation in supergravity and obtain a severe constraint on the symmetry breaking scale which is related with the tensor-to-scalar ratio. Depending on model parameters, it is possible that monopoles are sufficiently diluted to be free from current constraints but still observable by planned experiments.

hep-ph↗

arXiv2011

On Black Holes in Massive Gravity

In massive gravity the so-far-found black hole solutions on Minkowski space happen to convert horizons into a certain type of singularities. Here we explore whether these singularities can be avoided if space-time is not asymptotically Minkowskian. We find an exact analytic black hole (BH) solution which evades the above problem by a transition at large scales to self-induced de Sitter (dS) space-time, with the curvature scale set by the graviton mass. This solution is similar to the ones discovered by Koyama, Niz and Tasinato, and by Nieuwenhuizen, but differs in detail. The solution demonstrates that in massive GR, in the Schwarzschild coordinate system, a BH metric has to be accompanied by the Stückelberg fields with nontrivial backgrounds to prevent the horizons to convert into the singularities. We also find an analogous solution for a Reissner-Nordström BH on dS space. A limitation of our approach, is that we find the solutions only for specific values of the two free parameters of the theory, for which both the vector and scalar fluctuations loose their kinetic terms, however, we hope our solutions represent a broader class with better behaved perturbations.

hep-th↗

arXiv2011

Quantizing Horava-Lifshitz Gravity via Causal Dynamical Triangulations

We extend the discrete Regge action of causal dynamical triangulations to include discrete versions of the curvature squared terms appearing in the continuum action of (2+1)-dimensional projectable Horava-Lifshitz gravity. Focusing on an ensemble of spacetimes whose spacelike hypersurfaces are 2-spheres, we employ Markov chain Monte Carlo simulations to study the path integral defined by this extended discrete action. We demonstrate the existence of known and novel macroscopic phases of spacetime geometry, and we present preliminary evidence for the consistency of these phases with solutions to the equations of motion of classical Horava-Lifshitz gravity. Apparently, the phase diagram contains a phase transition between a time-dependent de Sitter-like phase and a time-independent phase. We speculate that this phase transition may be understood in terms of deconfinement of the global gravitational Hamiltonian integrated over a spatial 2-sphere.

hep-th↗

arXiv2011

Quantum Equivalence Principle Violations in Scalar-Tensor Theories

We study the equivalence principle and its violations by quantum effects in scalar-tensor theories that admit a conformal frame in which matter only couples to the spacetime metric. These theories possess Ward identities that guarantee the validity of the weak equivalence principle to all orders in the matter coupling constants. These Ward identities originate from a broken Weyl symmetry under which the scalar field transforms by a shift, and from the symmetry required to couple a massless spin two particle to matter (diffeomorphism invariance). But the same identities also predict violations of the weak equivalence principle relatively suppressed by at least two powers of the gravitational couplings, and imply that quantum corrections do not preserve the structure of the action of these theories. We illustrate our analysis with a set of specific examples for spin zero and spin half matter fields that show why matter couplings do respect the equivalence principle, and how the couplings to the gravitational scalar lead to the weak equivalence principle violations predicted by the Ward identities.

hep-th↗

arXiv2012

Jet Physics from Static Charges in AdS

Soft interactions with high-energy jets are explored in radial coordinates which exploit the approximately conformal behavior of perturbative gauge theories. In these coordinates, the jets, approximated by Wilson lines, become static charges in Euclidean AdS. The anomalous dimension of the corresponding Wilson line operator is then determined by the potential energy of the charges. To study these Wilson lines we introduce a "conformal gauge" which does not have kinetic mixing between radial and angular directions, and show that a number of properties of Wilson lines are reproduced through relatively simple calculations. For example, certain non-planar graphs involving multiple Wilson lines automatically vanish. We also discuss the linear growth of the charges' imaginary potential energy with separation, and a relationship between Wilson line diagrams and Witten diagrams.

hep-th↗

arXiv2011

The factorisation of glue and mass terms in SU(N) gauge theories

In this paper we investigate the structure of the glue in Zwanziger's gauge invariant expansion for the A^2-type mass term in Yang-Mills theory. We show how to derive this expansion, in terms of the inverse covariant Laplacian, and extend it to higher orders. In particular, we give an explicit expression, for the first time, for the next to next to leading order term. We further show that the expansion is not unique and give examples of the resulting ambiguity.

hep-th↗

arXiv2011

An anomalous hydrodynamics for chiral superfluid

Starting from low energy effective chiral Lagrangian with gauged Wess-Zumino Witten term, we have derived a hydrodynamic theory for chiral superfluid. It is a non-abelian hydrodynamics at zero temperature with only superfluid components. With an external electromagnetic field and baryonic and axial baryonic chemical potentials turned on, we are able to identify analogs of various anomaly induced term in normal hydrodynamics, including chiral vortical effect, chiral magnetic effect and chiral electric effect. As an example, we solved the hydrodynamic equations for the ground state and observed the chiral magnetic effect and chiral separation in the confined phase.

hep-ph↗

arXiv2011

Spectral-Function Sum Rules in Supersymmetry Breaking Models

The technique of Weinberg's spectral-function sum rule is a powerful tool for a study of models in which global symmetry is dynamically broken. It enables us to convert information on the short-distance behavior of a theory to relations among physical quantities which appear in the low-energy picture of the theory. We apply such technique to general supersymmetry breaking models to derive new sum rules.

hep-ph↗

arXiv2012

Density of states and Fisher's zeros in compact U(1) pure gauge theory

We present high-accuracy calculations of the density of states using multicanonical methods for lattice gauge theory with a compact gauge group U(1) on 4^4, 6^4 and 8^4 lattices. We show that the results are consistent with weak and strong coupling expansions. We present methods based on Chebyshev interpolations and Cauchy theorem to find the (Fisher's) zeros of the partition function in the complex beta=1/g^2 plane. The results are consistent with reweighting methods whenever the latter are accurate. We discuss the volume dependence of the imaginary part of the Fisher's zeros, the width and depth of the plaquette distribution at the value of beta where the two peaks have equal height. We discuss strategies to discriminate between first and second order transitions and explore them with data at larger volume but lower statistics. Higher statistics and even larger lattices are necessary to draw strong conclusions regarding the order of the transition.

hep-lat↗