arXiv subjects

T. Krajewski

Publications and source records attributed to T. Krajewski.

18 recordsLinked to original sources

arXiv2023

Duality of O(N) and Sp(N) random tensor models: tensors with symmetries

In a recent series of papers, a duality between orthogonal and symplectic random tensor models has been proven, first for quartic models and then for models with interactions of arbitrary order. However, the tensor models considered so far in the literature had no symmetry under permutation of the indices. In this paper, we generalize these results for tensors models with interactions of arbitrary order which further have non-trivial symmetry under the permutation of the indices. Totally symmetric and anti-symmetric tensors are thus treated as a particular case of our result.

math-ph↗

arXiv2023

Double scaling limit of the prismatic tensor model

In S. Giombi, I. Klebanov, F. Popov, S. Prakash and G. Tarnopolsky, {\it Phys. Rev.} {\bf D} 98 (2018) 10, 105005, a prismatic tensor model was introduced. We study here the diagrammatics and the double scaling limit of this model, using the intermediate field method. We explicitly exhibit the next-to-leading order Feynman graphs in the $1/N$ expansion. Using appropriate combinatorial tools, we further study the general term of the $1/N$ expansion and we compute the $2-$point function in the double scaling limit.

hep-th↗

arXiv2018

Non-Gaussian disorder average in the Sachdev-Ye-Kitaev model

We study the effect of non-Gaussian average over the random couplings in a complex version of the celebrated Sachdev-Ye-Kitaev (SYK) model. Using a Polchinski-like equation and random tensor Gaussian universality, we show that the effect of this non-Gaussian averaging leads to a modification of the variance of the Gaussian distribution of couplings at leading order in N. We then derive the form of the effective action to all orders. An explicit computation of the modification of the variance in the case of a quartic perturbation is performed for both the complex SYK model mentioned above and the SYK generalization proposed in D. Gross and V. Rosenhaus, JHEP 1702 (2017) 093.

hep-th↗

arXiv2016

Wigner law for matrices with dependent entries - a perturbative approach

We show that Wigner semi-circle law holds for Hermitian matrices with dependent entries, provided the deviation of the cumulants from the normalised Gaussian case obeys a simple power law bound in the size of the matrix. To establish this result, we use replicas interpreted as a zero-dimensional quantum field theoretical model whose effective potential obey a renormalisation group equation.

math-ph↗

arXiv2013

Renormalization group-like proof of the universality of the Tutte polynomial for matroids

In this paper we give a new proof of the universality of the Tutte polynomial for matroids. This proof uses appropriate characters of Hopf algebra of matroids, algebra introduced by Schmitt (1994). We show that these Hopf algebra characters are solutions of some differential equations which are of the same type as the differential equations used to describe the renormalization group flow in quantum field theory. This approach allows us to also prove, in a different way, a matroid Tutte polynomial convolution formula published by Kook, Reiner and Stanton (1999). This FPSAC contribution is an extended abstract.

math.CO↗

arXiv2011

ZnCoO Films by Atomic Layer Deposition - influence of a growth temperature on uniformity of cobalt distribution

We report on the structural, electrical and magnetic properties of ZnCoO thin films grown by Atomic Layer Deposition (ALD) method using reactive organic precursors of zinc and cobalt. As a zinc precursor we applied either dimethylzinc or diethylzinc and cobalt (II) acetyloacetonate as a cobalt precursor. The use of these precursors allowed us the significant reduction of a growth temperature to 300oC and below, which proved to be very important for the growth of uniform films of ZnCoO. Structural, electrical and magnetic properties of the obtained ZnCoO layers will be discussed based on the results of SIMS, SEM, EDS, XRD, AFM, Hall effect and SQUID investigations.

cond-mat.mtrl-sci↗

arXiv2008

Topological Graph Polynomials and Quantum Field Theory, Part I: Heat Kernel Theories

We investigate the relationship between the universal topological polynomials for graphs in mathematics and the parametric representation of Feynman amplitudes in quantum field theory. In this first paper we consider translation invariant theories with the usual heat-kernel-based propagator. We show how the Symanzik polynomials of quantum field theory are particular multivariate versions of the Tutte polynomial, and how the new polynomials of noncommutative quantum field theory are particular versions of the Bollobás-Riordan polynomials.

math-ph↗

arXiv2007

Quasi-quantum groups from Kalb-Ramond fields and magnetic amplitudes for strings on orbifolds

We present the general form of the operators that lift the group action on the twisted sectors of a bosonic string on an orbifold ${\cal M}/G$, in the presence of a Kalb-Ramond field strength $H$. These operators turn out to generate the quasi-quantum group $D_ω[G]$, introduced in the context of orbifold conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche. The 3-cocycle $ω$ entering in the definition of $D_ω[G]$ is related to $H$ by a series of cohomological equations in a tricomplex combining de Rham, Cech and group coboundaries. We construct magnetic amplitudes for the twisted sectors and show that $ω=1$ arises as a consistency condition for the orbifold theory. Finally, we recover discrete torsion as an ambiguity in the lift of the group action to twisted sectors, in accordance with previous results presented by E. Sharpe.

hep-th↗

arXiv2007

Quasi-quantum groups from strings

Motivated by string theory on the orbifold ${\cal M}/G$ in presence of a Kalb-Ramond field strength $H$, we define the operators that lift the group action to the twisted sectors. These operators turn out to generate the quasi-quantum group $D_ω[G]$, introduced in the context of conformal field theory by R. Dijkgraaf, V. Pasquier and P. Roche, with $ω$ a 3-cocycle determined by a series of cohomological equations in a tricomplex combining de Rham, uCech and group cohomologies. We further illustrate some properties of the quasi-quantum group from a string theoretical point of view.

hep-th↗

arXiv2006

Quantum field theory on projective modules

We propose a general formulation of perturbative quantum field theory on (finitely generated) projective modules over noncommutative algebras. This is the analogue of scalar field theories with non-trivial topology in the noncommutative realm. We treat in detail the case of Heisenberg modules over noncommutative tori and show how these models can be understood as large rectangular pxq matrix models, in the limit p/q->theta, where theta is a possibly irrational number. We find out that the modele is highly sensitive to the number-theoretical aspect of theta and suffers from an UV/IR-mixing. We give a way to cure the entanglement and prove one-loop renormalizability.

hep-th↗

arXiv2004

An algebraic Birkhoff decomposition for the continuous renormalization group

This paper aims at presenting the first steps towards a formulation of the Exact Renormalization Group Equation in the Hopf algebra setting of Connes and Kreimer. It mostly deals with some algebraic preliminaries allowing to formulate perturbative renormalization within the theory of differential equations. The relation between renormalization, formulated as a change of boundary condition for a differential equation, and an algebraic Birkhoff decomposition for rooted trees is explicited.

hep-th↗

arXiv2001

Exact solitons on noncommutative tori

We construct exact solitons on noncommutative tori for the type of actions arising from open string field theory. Given any projector that describes an extremum of the tachyon potential, we interpret the remaining gauge degrees of freedom as a gauge theory on the projective module determined by the tachyon. Whenever this module admits a constant curvature connection, it solves exactly the equations of motion of the effective string field theory. We describe in detail such a construction on the noncommutative tori. Whereas our exact solution relies on the coupling to a gauge theory, we comment on the construction of approximate solutions in the absence of gauge fields.

hep-th↗

arXiv1999

U_{q}(sl_{2}) at fourth root of unity

In this paper, we study finite dimensional quotients of the Hopf algebra U_{q}(sl_{2}) at fourth root of unity. We give explicitly all the corresponding automorphisms, real forms and idempotents.

math.QA↗

arXiv1999

Distances in Finite Spaces from Noncommutative Geometry

Following the general principles of noncommutative geometry, it is possible to define a metric on the space of pure states of the noncommutative algebra generated by the coordinates. This metric generalizes the usual Riemannian one. We investigate some general properties of this metric in the finite commutative case which corresponds to a metric on a finite set, and also give some examples of computations in both commutative and noncommutative cases.

hep-th↗

arXiv1999

Noncommutative geometry and fundamental interactions

This PhD thesis aims at describing the applications of noncommutative geometry to particle physics and quantum field theory. It includes a brief survey of the basic principles and definitions of noncommutative geometry such as spectral triples, differential calculus or gauge theories on projective modules. Within this framework, The index theorem and cyclic homology are applied to the probe of topologically non trivial properties of Chern-Simons and Yang-Mills action functionals in dimension 3 and 4. Following earlier work on the standard model in noncommutative geometry, it also provides a general study of all Yang-Mills-Higgs models based on space-times structures which are the product of usual space-time by a discrete space, with emphasis on the physical properties of the resulting theories. Finally, the last part is devoted to the development of classical and quantum gauge theory on the noncommutative torus in any dimension. It includes a discussion of topological properties and symmetries of the action as well as its perturbative quantization.

math-ph↗

arXiv1999

Perturbative quantum gauge fields on the noncommutative torus

Using standard field theoretical techniques, we survey pure Yang-Mills theory on the noncommutative torus, including Feynman rules and BRS symmetry. Although in general free of any infrared singularity, the theory is ultraviolet divergent. Because of an invariant regularization scheme, this theory turns out to be renormalizable and the detailed computation of the one loop counterterms is given, leading to an asymptoticaly free theory. Besides, it turns out that non planar diagrams are overall convergent when $θ$ is irrational.

hep-th↗

arXiv1998

Gauge invariance of the Chern-Simons action in noncommutative geometry

In complete analogy with the classical case, we define the Chern-Simons action functional in noncommutative geometry and study its properties under gauge transformations. As usual, the latter are related to the connectedness of the group of gauge transformations. We establish this result by making use of the coupling between cyclic cohomology and K-theory and prove, using an index theorem, that this coupling is quantized in the case of the noncommutative torus.

math-ph↗

arXiv1998

Constraints on the scalar potential from spectral action principle

Using noncommutative geometry, the standard tools of differential geometry can be extended to a broad class of spaces whose coordinates are noncommuting operators acting on a Hilbert space. In the simplest case of coordinates being matrix valued functions on space-time, the standard model of particle physics can be reconstructed out of a few basic principles. Following these ideas, we investigate the general case of models arising from matrices and give the resulting constraints on the scalar potential and gauge couplings constants, as well as some relations between fermionic and bosonic masses.

hep-th↗