Cavitation in holographic sQGP

We study the possibility of cavitation in the non-conformal N=^2?SU(N) theory which is a mass deformation of N=4SU(N) Yang-Mills theory. The second order transport coefficients are known from the numerical work using AdS/CFT by Buchel and collaborators. Using these and the approach of Rajagopal and Tripuraneni, we investigate the flow equations in a (1+1)-dimensional boost invariant set up. We find that the string theory model does not exhibit cavitation before phase transition is reached. We give a semi-analytic explanation of this finding.     

Two-pion production in photon-photon collisions

We calculate within chiral perturbation theory the cross section for γγ→π⁰π⁰ and γγ→π⁺π⁻ to next-to-leading order. The first process only depends on the one-loop contributions and forms a test of chiral perturbation theory. We also calculate the pion electromagnetic form factor and compare it to recent data.     

Non-perturbative construction of 2D and 4D supersymmetric Yang-Mills theories with 8 supercharges

In this paper, we consider two-dimensional N=(4,4) supersymmetric Yang-Mills (SYM) theory and deform it by a mass parameter M with keeping all supercharges. We further add another mass parameter m in a manner to respect two of the eight supercharges and put the deformed theory on a two-dimensional square lattice, on which the two supercharges are exactly preserved. The flat directions of scalar fields are stabilized due to the mass deformations, which gives discrete minima representing fuzzy spheres. We show in the perturbation theory that the lattice continuum limit can be taken without any fine tuning. Around the trivial minimum, this lattice theory serves as a non-perturbative definition of two-dimensional N=(4,4) SYM theory. We also discuss that the same lattice theory realizes four-dimensional N=2U(k) SYM on R²×(Fuzzy R²) around the minimum of k-coincident fuzzy spheres.     

Vacuum Stability of the Wrong Sign (−ϕ 6) Scalar Field Theory

We apply the effective potential method to study the vacuum stability of the bounded from above (?? ⁶) (unstable) quantum field potential. The stability (?E/?b = 0) and the mass renormalization (? ² E/?b ² = M ²) conditions force the effective potential of this theory to be bounded from below (stable). Since bounded from below potentials are always associated with localized wave functions, the algorithm we use replaces the boundary condition applied to the wave functions in the complex contour method by two stability conditions on the effective potential obtained. To test the validity of our calculations, we show that our variational predictions can reproduce exactly the results in the literature for the \(\mathcal {PT}\) -symmetric ? ⁴ theory. We then extend the applications of the algorithm to the unstudied stability problem of the bounded from above (?? ⁶) scalar field theory where classical analysis prohibits the existence of a stable spectrum. Concerning this, we calculated the effective potential up to first order in the couplings in d space-time dimensions. We find that a Hermitian effective theory is instable while a non-Hermitian but \(\mathcal {PT}\) -symmetric effective theory characterized by a pure imaginary vacuum condensate is stable (bounded from below) which is against the classical predictions of the instability of the theory. We assert that the work presented here represents the first calculations that advocates the stability of the (?? ⁶) scalar potential.     

Aspects of Pohlmeyer reduction for superstrings in AdS 5 × S 5

We review some recent work on Pohlmeyer reduced theory associated to superstring theory in AdS ₅ × S ⁵. We discuss the S-matrix of the reduced theory and also the computation of the 2-loop correction to the partition function in a non-trivial background.     

On loop corrections to string theory effective actions

We make some comments concerning the structure of loop corrections to the effective action (EA) for massless fields of a string. The singular part of the α′→0 limit of the one-loop EA in the open (super)string theory is studied and is shown to be in correspondence with the ultraviolet divergent part of the one-loop effective action in the (super) Yang-Mills theory. In particular, we reproduce the known result about the absence of Λ^D−4 F_μν² one-loop infinities in D = 26 Yang-Mills theory starting from the open Bose string theory. We also discuss the path integral representation for EA (EA = generalized partition function for the σ-model) and use it to compute the open string theory EA on the disc and the annulus.     

Spinor theory of general relativity without elementary gravitons

We propose a generally covariant and locally Lorentz invariant theory of a Majorana spinor field ψ_μ^α. Our theory has no elementary spin-2 quanta, but does reproduce Einstein's general relativity as a classical solution. We compare this situation to the possibility of finding classical monopoles in a gauge theory, even though no such elementary object is introduced at the outset.     

Hyperfine structure in hydrogen and helium ion

QED theory of the hyperfine splitting of the 1s and 2s state in hydrogen isotopes and helium-3 ion is considered. We develop an accurate theory of a specific difference 8E_HFS(2s)−E_HFS(1s). We take into account higher-order QED and nuclear structure effects. In particular, we found the vacuum polarization contribution in order α(Zα)³E_F and examined the recoil contribution in order (Zα)³m/M and thus completed a calculation of the fourth order QED corrections. The higher-order nuclear structure contributions were also analysed. The theoretical predictions reported here are now of a higher accuracy than the experiment. The study of the difference provides the most accurate test (at a level of a part in 10⁸) of the QED theory of ns HFS up to date. The theory agrees with most of the experimental data.     

CPN−1 coupled to gauge fields: Mean field theory and monte carlo results

We define a two parameter lattice field theory which interpolates between the O (2N) Heisenberg model, pure U(1) gauge theory, and a lattice version of the CP^N?1 model. The phase diagram in space-time dimension d=4 is obtained by Monte Carlo simulation on a 4⁴ lattice, and the nature of the phases is discussed in mean field approximation.     

Hydrodynamic Limit of a B.G.K. Like Model on Domains with Boundaries and Analysis of Kinetic Boundary Conditions for Scalar Multidimensional Conservation Laws

In this paper we study the hydrodynamic limit of a B.G.K. like kinetic model on domains with boundaries via BV _loc theory. We obtain as a consequence existence results for scalar multidimensional conservation laws with kinetic boundary conditions. We require that the initial and boundary data satisfy the optimal assumptions that they all belong to L ¹∩L ^∞ with the additional regularity assumptions that the initial data are in BV _loc . We also extend our hydrodynamic limit analysis to the case of a generalized kinetic model to account for forces effects and we obtain as a consequence the existence theory for conservation laws with source terms and kinetic boundary conditions.     

The electric screening mass in scalar electrodynamics at high temperature

We study the screening of static electric fields in massless scalar electrodynamics at high temperature and zero chemical potential. Effective field theory methods are used to separate the contributions from the momentum scales T and eT to the electric screening mass. The effects of the distance scale 1/T are encoded in the parameters of an effective three-dimensional field theory. The parameters of the effective Lagrangian can be written as a power series in e ². The contribution to physical quantities from the scale 1/eT can be calculated from perturbation theory in the effective theory and is an expansion in e starting at e ³. The electric screening mass squared is computed to order e ⁴.     

A non-perturbative analysis of symmetry breaking in two-dimensional φ4 theory using periodic field methods

We describe the generalization of spherical field theory to other modal expansion methods. The main approach remains the same, to reduce a d-dimensional field theory into a set of coupled one-dimensional systems. The method we discuss here uses an expansion with respect to periodic-box modes. We apply the method to φ⁴ theory in two dimensions and compute the critical coupling and critical exponents. We compare with lattice results and predictions via universality and the two-dimensional Ising model.     

d-Wave superconductivity via buckling-like phonon mode

We follow the classic strong-coupling theory of superconductivity through electron-phonon interaction with a buckling-like phonon mode. We find a nonzero d-wave order parameter in the sense of the Eliashberg theory. We derive a zero temperature gap Δ(0,π) at the gap edge versus the electron-phonon coupling strength g² relation. We find that large enough value for Δ(0,π) as compared to those of high-T_c superconductors cannot be realized in the electron-buckling-like-phonon coupling on the CuO₂ planes.     

Logarithmic correlation functions in two-dimensional turbulence

We consider the correlation functions of two-dimensional turbulence in the presence and absence of a three-dimensional perturbation, by means of conformal field theory. In the presence of three-dimensional perturbation, we show that in the strong coupling limit of a small scale random force, there is some logarithmic factor in the correlation functions of velocity stream functions. We show that the logarithmic conformal field theory c_8,1 describes the 2D-turbulence both in the absence and in the presence of the perturbation. We obtain the energy spectrum E(k) ∼ k^−5.125 ln(k) for perturbed 2D-turbulence and E(k) ∼ k⁻⁵ ln(k) for unperturbed turbulence. Recent numerical simulation and experimental results confirm our prediction.     

External gravitational interactions in quantum field theory

We consider the renormalization of Green's functions of λφ⁴ quantum field theory in an external gravitational field specified by the metric tensor g^μν(y). Green's functions Γ^(n,3) describing the interaction of j scalar particles to arbitrary order n in the gravitational field are shown to be made finite by the standard renormalizations of the flatspace theory and a renormalization of the coefficient of the improvement term in the action functional. These results in φ⁴ theory can be extended to all renormalizable field theories.     

Renormalizability and asymptotic freedom in quantum gravity

We discuss a previously proposed renormalizable theory of gravity involving R²_μν, and N massless fermion (vector boson) fields in which the unitarity problem is resolved within a $\text{1}\text{N}$ expansion. The infrared limit is precisely Einstein's theory, but the high-energy behavior is determined by the dimensionless, asymptotically free coupling of the R²_μν. Various attractive possible consequences of the theory are pointed out.     

Calculation of the glueball mass spectrum ofSU (2) andSU (3) non-abelian lattice gauge theories II:SU (3)

We calculate the glueball mass spectrum in theSU (3) lattice regularized gauge theory. We find fourlight glueballs: the 0⁺⁺, 2⁺⁺, 0^?+ and, most interestingly from the experimental point of view, the oddball 1^?+. We calculate the 0⁺⁺ and 2⁺⁺ masses over a range of β values and find thatboth states conform to continuum renormalization group behaviour to a very significant degree. The question of metastable states and temperature is addressed in detail. Finally we discuss and resolve contrary claims in the recent literature.     

Threshold neutral pion photoproduction off the tri-nucleon to O(q4)

We calculate the electromagnetic neutral pion production off tri-nucleon bound states (³H, ³He) at threshold in chiral nuclear effective field theory to fourth order in the standard heavy baryon counting. We show that the fourth-order two-nucleon corrections to the S-wave multipoles at threshold are very small. This implies that a precise measurement of the S-wave cross section for neutral pion production off ³He allows for a stringent test of the chiral perturbation theory prediction for the S-wave electric multipole $E_{0+}^{\pi^0 n}$ .     

Chern–Simons theory with vector fermion matter

We study three-dimensional conformal field theories described by U(N) Chern?CSimons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger?CDyson equation in light-cone gauge, we compute the exact planar free energy of the theory at finite temperature on ?² as a function of the ??t?Hooft coupling ??=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at |??|=1; the conformal theory does not exist for |??|>1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N. We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three-point functions up to two loops. We also discuss a light-cone Hamiltonian formulation of this theory where a W _?? algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U(1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory.     

Light-cone quantisation of the Liouville and Toda field theories

The Toda field is a multicomponent field in two space-time dimensions satisfying a generalisation of the Liouville equation ?²? + exp ? = 0. We define the quantum field theory, and solve for the fields in terms of their initial values on a forward light-cone, demonstrating that our solution is regular. We give an explicit result for the Liouville equation which is the quantum version of the well-known classical solution. We also discuss the energy-momentum spectrum, and the conformal properties of the theory.