arXiv subjects

Blazej Ruba

Publications and source records attributed to Blazej Ruba.

6 recordsLinked to original sources

arXiv2022

Homological invariants of Pauli stabilizer codes

We study translationally invariant Pauli stabilizer codes with qudits of arbitrary, not necessarily uniform, dimensions. Using homological methods, we define a series of invariants called charge modules. We describe their properties and physical meaning. The most complete results are obtained for codes whose charge modules have Krull dimension zero. This condition is interpreted as mobility of excitations. We show that it is always satisfied for translation invariant 2D codes with unique ground state in infinite volume, which was previously known only in the case of uniform, prime qudit dimension. For codes all of whose excitations are mobile we construct a $p$-dimensional excitation and a $(D-p-1)$-form symmetry for every element of the $p$-th charge module. Moreover, we define a braiding pairing between charge modules in complementary degrees. We discuss examples which illustrate how charge modules and braiding can be computed in practice.

math-ph↗

arXiv2021

Nilpotent symmetries as a mechanism for Grand Unification

In the classic Coleman--Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact -- U(1) -- component, a Lorentz -- SL(2,C) -- component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman--Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

gr-qc↗

arXiv2020

Super Quantum Airy Structures

We introduce super quantum Airy structures, which provide a supersymmetric generalization of quantum Airy structures. We prove that to a given super quantum Airy structure one can assign a unique set of free energies, which satisfy a supersymmetric generalization of the topological recursion. We reveal and discuss various properties of these supersymmetric structures, in particular their gauge transformations, classical limit, peculiar role of fermionic variables, and graphical representation of recursion relations. Furthermore, we present various examples of super quantum Airy structures, both finite-dimensional -- which include well known superalgebras and super Frobenius algebras, and whose classification scheme we also discuss -- as well as infinite-dimensional, that arise in the realm of vertex operator super algebras.

math-ph↗

arXiv2020

Constraints of kinematic bosonization in two and higher dimensions

Contrary to the common wisdom, local bosonizations of fermionic systems exist in higher dimensions. Interestingly, resulting bosonic variables must satisfy local constraints of a gauge type. They effectively replace long distance exchange interactions. In this work we study in detail the properties of such a system which was proposed a long time ago. In particular, dependence of the constraints on lattice geometry and fermion multiplicity is further elaborated and is now classified for all two dimensional, rectangular lattices with arbitrary sizes. For few small systems the constraints are solved analytically and the complete spectra of reduced spin hamiltonias are shown to agree with the original fermionic ones. The equivalence is extended to fermions in an external Wegner $Z_2$ field. It is also illustrated by an explicit calculation for a particular configuration of Wegner variables. Finally, a possible connection with the recently proposed web of dualities is discussed.

hep-lat↗

arXiv2020

Characterization of Null Geodesics on Kerr Spacetimes

We consider null geodesics in the exterior region of a subextremal Kerr spacetime. We show that most well-known fundamental properties of null geodesics can be represented on one plot. In particular, one can see immediately that the ergoregion and trapping are separated in phase space. Furthermore, we show that from the point of view of any timelike observer outside of the black hole, trapping can be understood as a smooth set of spacelike directions on the celestial sphere of the observer. Finally, we discuss some applications of these insights.

gr-qc↗

arXiv2018

Beyond Complex Langevin Equations: a Progress Report

After a short review of one of proposals to avoid complex stochastic processes in Complex Langevin studies, the recent progress in the former is reported. In particular, the new developments allow now to construct positive and normalizable representations for gaussian quantum mechanical, as well as field theoretical, path integrals directly in the Minkowski time. A relation to the idea of thimbles is also discussed.

hep-lat↗