abstract

The eigenvalue density of a Wilson loop matrix \(W\) associated with a simple loop in two-dimensional Euclidean SU\((N)\) Yang–Mills theory undergoes a phase transition at a critical size in the infinite-\(N\) limit. The averages of \(\det (z-W)^{-1}\) and \(\det (1+uW)/(1-vW)\) at finite \(N\) lead to two different smoothed out expressions. It is shown by a saddle-point analysis that both functions tend to the known singular result at infinite \(N\).

abstract

We consider large \(N\) pure gauge lattice QCD on a cubical torus in \(2+1\) dimensions. The theory has four continuum phases: \(0c\), \(1c\), \(2c\) and \(3c\), where the numeral denotes the number of lattice directions with broken center symmetry. We show through numerical calculation on lattices of size \(2\leq L\leq 8\) that \(1c\)–\(2c\) and \(2c\)–\(3c\) phase transitions are weak first order. Some remarks are made about the nature of the \(0c\)–\(1c\) phase transition.

abstract

We present the results of a mixed action approach, employing dynamical twisted mass fermions in the sea sector and overlap valence fermions, with the aim of testing the continuum limit scaling behaviour of physical quantities, taking the pion decay constant as an example. To render the computations practical, we impose for this purpose a fixed finite volume with lattice size \(L\approx 1.3\) fm. We also briefly review the techniques we have used to deal with overlap fermions.

abstract

We apply chiral quark model with momentum dependent quark mass to two kinds of nonperturbative objects. These are: photon Distribution Amplitudes which we calculate up to twist-4 in tensor, vector and axial channels and pion–photon Transition Distribution Amplitudes together with related form factors. Where possible we compare our results with experimental data.

abstract

We start from recalling the limited and descriptive character of our theories, and point out the existence of a tension between relativity and quantum physics. It is then argued that some quantum features of the Standard Model may be understood when the concept of arena used for the description of physical processes is changed from relativistic ‘spacetime’ to nonrelativistic ‘phase-space \(+\) time’. The phase-space form \({x}^2+{p}^2\), which constitutes a natural generalization of 3D invariants \({x}^2\) and \({p}^2\), is linearized á la Dirac, with \(x_k\) and \(p_j\) satisfying standard commutation relations. This leads to a quantum-level structure related to phase space, and to the appearance of new quantum numbers. The latter are identified with internal quantum numbers characterizing the structure of a single quark–lepton generation. The approach provides a preonless interpretation of the Harari–Shupe model, and leads both to a different view on the concept of quark mass and to the emergence of quark-confining strings.

abstract

We introduce Weinberg’s idea of asymptotic safety and pave the way towards an asymptotically safe chiral Yukawa system with a U\((N_{\rm L})_{\rm L}\otimes \)U\((1)_{\rm R}\) symmetry in a leading order derivative expansion using nonperturbative functional RG equations. As a toy model sharing important features with the standard model we explicitely discuss \(N_{\rm L}=10\) for which we find a non-Gaussian fixed point and compute its critical exponents. We observe a reduced hierarchy problem as well as predictions for the toy Higgs and the toy top mass.

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We prove the existence of a limit of the finite volume probability measures generated by tree growth rules in Ford’s alpha model of phylogenetic trees. The limiting measure is shown to be concentrated on the set of trees consisting of exactly one infinite spine with finite, identically and independently distributed outgrowths.

abstract

The causal dynamical triangulations (CDT) program has for the first time allowed for path-integral computation of correlation functions in full general relativity without symmetry reductions and taking into account Lorentzian signature. One of the most exciting recent results in CDT is the strong agreement of these computations with (minisuperspace) path integral calculations in quantum cosmology. Herein I will describe my current project to compute minisuperspace (Friedman–Robertson–Walker) path integrals with a range of different measures corresponding to various factor orderings of the Friedman–Robertson–Walker Hamiltonian. The aim is to compare with CDT results and ask whether CDT can shed light on factor-ordering ambiguities in quantum cosmology models.

abstract

We present an analytic solution of the Riemann problem for the equations of relativistic hydrodynamics with the ultra-relativistic equation of state and non-zero tangential velocities. A 3 dimensional numerical code solving such equations is described and then tested against the analytic solution.

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In this talk I summarize briefly recent results of joint work with P. Bizoń, T. Chmaj and S. Zając, on the nonlinear origin of the power-law tails in the long-time evolution of self-gravitating massless fields. We focus on a spherically symmetric massless scalar field and wave map matter coupled to gravity. Using third-order perturbation method we derive explicit expressions for the tail (the decay rate and the amplitude) for solutions starting from small initial data and we verify this prediction via numerical integration of the full system of Einstein field equations. Our results show that the nonlinear effects can dominate the late time asymptotics.

abstract

The author shows how to construct a class of Lagrangians for relativistic dynamical systems described by position and a single spinor. One arrives at it by imposing three requirements: \((i)\) Hamilton action should be reparametrization invariant, \((ii)\) the number of dimensional parameters should be minimal, \((iii)\) the spinor phase should be a cyclic variable. In more detail in this paper are discussed the Lagrangians which depend on position and the spinor’s null vector only. An interesting relation of a Hessian determinant and Casimir invariants for such objects leads to the conclusion that no fundamental objects of this kind exist with worldlines uniquely determinable from the Hamilton action and the initial conditions. This unexpected result poses the general question about existence of classical fundamental dynamical systems with well posed Cauchy problem.

abstract

Oscillons are well localized, almost periodic and surprisingly long living states in classical field theories. We present a short overview of their basic properties and dynamics in \(1+1\) dimension. During collisions with kinks they behave as massive bodies which can reflect the kink or increase kink’s kinetic energy. Oscillons can also undergo so-called negative radiation pressure.

abstract

In this article we present the cut Fock space approach to the \(D\!=\!d +\!1\!=\!2\), Supersymmetric Yang–Mills Quantum Mechanics (SYMQM). We start by briefly introducing the main features of the framework. We concentrate on those properties of the method which make it a convenient set up not only for numerical calculations but also for analytic computations. In the main part of the article a sample of results are discussed, namely, analytic and numerical analysis of the \(D=2\), SYMQM systems with SU(2) and SU(3) gauge symmetry.

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We investigate \((2+1)\)-dimensional quiver Chern–Simons theories that arise from the study of M2-branes probing toric Calabi–Yau 4-folds. These theories can be elegantly described using brane tilings. We present several theories that admit a tiling description and give details of these theories including the toric data of their mesonic moduli space, the structure of their Master space and their baryonic moduli space. Where different toric phases are known, we exhibit the equivalence between the vacua. We identify some of the mesonic moduli spaces as cones over smooth toric Fano 3-folds.

abstract

We review the noncommutative gravity of Wess et al. (Class. Quantum Grav. 22, 3511 (2005) and Class. Quantum Grav. 23, 1883 (2006)) and discuss its physical applications. We define noncommutative symmetry reduction and construct deformed symmetric solutions of the noncommutative Einstein equations. We apply our framework to find explicit deformed cosmological and black hole solutions and discuss their phenomenology.

abstract

The gauge approach to the theory of gravity has been widely discussed as an alternative to standard general relativity. The Poincaré group, as a symmetry group of all relativistic theories in the absence of gravitation, constitutes the most natural candidate for a gauge group. Although the Poincaré gauge theory of gravity has been elaborated over the years and cast into a beautiful formal framework, some fundamental problems have remained unsolved. One of them concerns the inclusion of matter. The minimal coupling procedure, which is employed in standard Yang–Mills theories, appears to be ambiguous in the case of gravity. We propose a slight modification of this procedure, which removes the ambiguity. Our modification justifies some earlier results concerning the consequences of the Poincaré gauge theory of gravity. In particular, the predictions of Einstein–Cartan theory with fermionic matter are rendered unique. We recall the earlier proposed solution based on modified volume-forms. The advantage of our modification is that the predictions of the theory are not radically changed. Basically, this modification simply justifies the results that were obtained partly “by chance” in the hitherto prevailing accounts on the Einstein–Cartan theory. The only difference in the predictions, when compared to the standard treatment, concerns the Proca field in the presence of gravity. The “torsion singularities” that occur there are shifted towards other values of the field.