Searcharxiv⌕ Search

arXiv subjects

Karl-Georg Schlesinger

Publications and source records attributed to Karl-Georg Schlesinger.

At least 19 recordsLinked to original sources
arXiv2015

Notes on the firewall paradox, complexity, and quantum theory

We investigate what it means to apply the solution, proposed to the firewall paradox by Harlow and Hayden, to the famous quantum paradoxes of Schödinger's Cat and Wigner's Friend if ones views these as posing a thermodynamic decoding problem (as does Hawking radiation in the firewall paradox). The implications might point to a relevance of the firewall paradox for the axiomatic and set theoretic foundations underlying mathematics. We reconsider in this context the results of Benioff on the foundational challenges posed by the randomness postulate of quantum theory. A central point in our discussion is that one can mathematically not naturally distinguish between computational complexity (as central to the approach of Harlow and Hayden and further developed by Susskind) and proof theoretic complexity (since they represent the same concept on a Turing machine), with the latter being related to a finite bound on Kolmogorov entropy (due to Chaitin incompleteness).

physics.gen-ph↗
arXiv2014

Entropy, heat, and Gödel incompleteness

Irreversible phenomena, such as the production of entropy and heat, arise from fundamental reversible dynamics because the forward dynamics is too complex, in the sense that it becomes impossible to provide the necessary information to keep track of the dynamics. On a heuristic level, this is well captured by coarse graining. We suggest that on a fundamental level the impossibility to provide the necessary information might be related to the incompleteness results of Gödel. This would hold interesting implications for both, mathematics and physics.

physics.gen-ph↗
arXiv2011

Eight dimensional physics and the Langlands program - A short note

We argue that a special step in the chain of dualities used in [Tan 2008] implicitly suggests to view Langlands duality as being fundamentally rooted in an eight-dimensional theory on the F-theory 7- brane. We give further arguments why such an eight-dimensional per- spective might be of interest.

hep-th↗
arXiv2009

A physics perspective on geometric Langlands duality

We review the approach to the geometric Langlands program for algebraic curves via S-duality of an N=4 supersymmetric four dimensional gauge theory, initiated by Kapustin and Witten in 2006. We sketch some of the central further developments. Placing this four dimensional gauge theory into a six dimensional framework, as advocated by Witten, holds the promise to lead to a formulation which makes geometric Langlands duality a manifest symmetry (like coavariance in differential geometry). Furthermore, it leads to an approach toward geometric Langlands duality for algebraic surfaces, reproducing and extending the recent results of Braverman and Finkelberg.

hep-th↗
arXiv2006

The universality question for noncommutative quantum field theory

Present day physics rests on two main pillars: General relativity and quantum field theory. We discuss the deep and at the same time problematic interplay between these two theories. Based on an argument by Doplicher, Fredenhagen, and Roberts, we propose a possible universality property for noncommutative quantum field theory in the sense that any theory of quantum gravity should involve quantum field theories on noncommutative space-times as a special limit. We propose a mathematical framework to investigate such a universality property and start the discussion of its mathematical properties. The question of its connection to string theory could be a starting point for a new perspective on string theory.

hep-th↗
arXiv2006

Does the fivebrane have a nonclassical BV-structure?

The fivebrane in M-theory comes equipped with a higher order gauge field which should have a formulation in terms of a 2-gerbe on the fivebrane. One can pose the question if the BV-quantization scheme for such a higher order gauge theory should differ from the usual BV-algebra structure. We give an algebraic argument that this should, indeed, be the case and a fourth order equation should appear as Master equation, in this case. We also discover a second order term in this equation which seems to indicate that deformation theory (i.e. solving the Master equation) in this case involves a nonlinear algebraic theory which goes beyond complexes and cohomology.

hep-th↗
arXiv2005

On deformation theory of quantum vertex algebras

We study an algebraic deformation problem which captures the data of the general deformation problem for a quantum vertex algebra. We derive a system of coupled equations which is the counterpart of the Maurer-Cartan equation on the usual Hochschild complex of an assocative algebra. We show that this system of equations results from an action principle. This might be the starting point for a perturbative treatment of the deformation problem of quantum vertex algebras. Our action generalizes the action of the Kodaira-Spencer theory of gravity and might therefore also be of relevance for applications in string theory.

hep-th↗
arXiv2004

The universal envelope of the topological closed string BRST-complex

We construct a universal envelope for any Poisson- and Gerstenhaber algebra. While the deformation theory of Poisson algebras seems to be partially trivial, results from string- and M-theory suggest a rich deformation theory of Gerstenhaber algebras. We apply our construction in this case to well known questions on the topological closed string BRST-complex. Finally, we find a similar algebraic structure, as for the universal envelope, in the SU(2)-WZW model.

hep-th↗
arXiv2004

A remark on the motivic Galois group and the quantum coadjoint action

It was suggested by Kontsevich that the Grothendieck-Teichmueller group GT should act on the Duflo isomorphism of su(2) but the corresponding realization of GT turned out to be trivial. We show that a solvable quotient of the motivic Galois group - which is supposed to agree with GT - is closely related to the quantum coadjoint action on U_q(sl_2) for q a root of unity, i.e. in the quantum group case one has a nontrivial realization of a quotient of the motivic Galois group. From a discussion of the algebraic properties of this realization we conclude that in more general cases than U_q(sl_2) it should be related to a quantum version of the motivic Galois group. Finally, we discuss the relation of our construction to quantum field and string theory and explain what we believe to be the "physical reason" behind this relation between the motivic Galois group and the quantum coadjoint action. This might be a starting point for the generalization of our construction to more involved examples.

hep-th↗
arXiv2004

A duality Hopf algebra for holomorphic N=1 special geometries

We find a self-dual noncommutative and noncocommutative Hopf algebra acting as a universal symmetry on the modules over inner Frobenius algebras of modular categories (as used in two dimensional boundary conformal field theory) similar to the Grothendieck-Teichmueller group GT as introduced by Drinfeld as a universal symmetry of quasitriangular quasi-Hopf algebras. We discuss the relationship to a similar self-dual, noncommutative, and noncocommutative Hopf algebra, previously found as the universal symmetry of trialgebras and three dimensional extended topological quantum field theories. As an application of our result, we get a transitive action of a sub-Hopf algebra of the latter universal symmetry algebra on the relative period matrices of holomorphic N=1 special geometries.

math.CT↗
arXiv2003

A universal symmetry structure in open string theory

In this paper, we arrive from different starting points at the conclusion that the symmetry given by an action of the Grothendieck-Teichmueller group GT on the so called extended moduli space of string theory can not be physical - in the sense that it does not survive the inclusion of general nonperturbative vacua given by boundary conditions on the level of two dimensional conformal field theory - but has to be extended to a quantum symmetry given by a self-dual, noncommutative, and noncocommutative Hopf algebra. First, we show that a class of two dimensional boundary conformal field theories always uniquely defines a trialgebra and find the above mentioned Hopf algebra as the universal symmetry of such trialgebras (in analogy to the definition of GT as the universal symmetry of quasi-triangular quasi-Hopf algebras). Second, we argue in a more heuristic approach that this Hopf algebra symmetry can also be found in a more geometric picture using the language of gerbes.

hep-th↗
arXiv2002

On a quantum analog of the Grothendieck-Teichmueller group

We introduce a noncommutative and noncocommutative Hopf algebra which takes for certain Hopf categories (and therefore braided monoidal bicategories) a similar role as the Grothendieck- Teichmueller group for quasitensor categories. We also give a result which highly restricts the possibility for similar structures for even higher weak n-categories than bicategories by showing that these structures would not allow for any nontrivial deformations. Finally, we give an explicit description of the elements of this Hopf algebra.

math.QA↗
arXiv2001

Some remarks on q-deformed multiple polylogarithms

We introduce general q-deformed multiple polylogarithms which even in the dilogarithm case differ slightly from the deformation usually discussed in the literature. The merit of the deformation as suggested, here, is that q-deformed multiple polylogarithms define an algebra, then (as in the undeformed case). For the special case of q-deformed multiple zeta-values, we show that there exists even a noncommutative and noncocommutative Hopf algebra structure which is a deformation of the commutative Hopf algebra structure which one has in the classical case. Finally, we discuss the possible correspondence between q-deformed multiple polylogarithms and a noncommutative and noncocommutative self-dual Hopf algebra recently introduced by the author as a quantum analog of the Grothendieck-Teichmueller group.

math.QA↗
arXiv2001

Spinfoam models for M-theory

We use the approach to generate spin foam models by an auxiliary field theory defined on a group manifold (as recently developed in quantum gravity and quantization of BF-theories) in the context of topological quantum field theories with a 3-form field strength. Topological field theories of this kind in seven dimensions are related to the superconformal field theories which live on the worldvolumes of fivebranes in M-theory. The approach through an auxiliary field theory for spinfoams gives a topology independent formulation of such theories.

hep-th↗
arXiv2001

On a noncommutative deformation of the Connes-Kreimer algebra

We study a noncommutative deformation of the commutative Hopf algebra of rooted trees which was shown by Connes and Kreimer to be related to the mathematical structure of renormalization in quantum field theories. The requirement of the existence of an antipode for the noncommutative deformation leads to a natural extension of the algebra. Noncommutative deformations of the Connes-Kreimer algebra might be relevant for renormalization of field theories on noncommutative spaces and there are indications that in this case the extension of the algebra might be linked to a mixing of infrared and ultraviolet divergences. We give also an argument that for a certain class of noncommutative quantum field theories renormalization should be linked to a noncommutative and noncocommutative self-dual Hopf algebra which can be seen as a noncommutative counterpart of the Grothendieck- Teichmueller group.

math.QA↗
arXiv2001

A suggestion for an integrability notion for two dimensional spin systems

We suggest that trialgebraic symmetries migth be a sensible starting point for a notion of integrability for two dimensional spin systems. For a simple trialgebraic symmetry we give an explicit condition in terms of matrices which a Hamiltonian realizing such a symmetry has to satisfy and give an example of such a Hamiltonian which realizes a trialgebra recently given by the authors in another paper. Besides this, we also show that the same trialgebra can be realized on a kind of Fock space of q-oscillators, i.e. the suggested integrability concept gets via this symmetry a close connection to a kind of noncommutative quantum field theory, paralleling the relation between the integrability of spin chains and two dimensional conformal field theory.

hep-th↗
arXiv2000

On the universality of string theory

String theory is accused by some of its critics to be a purely abstract mathematical discipline, having lost the contact to the simple yet deeply rooted questions which physics provided until the beginning of this century. We argue that, in contrary, there are indications that string theory might be linked to a fundamental principle of a quantum computational character. In addition, the nature of this principle might be capable to provide some new insight into the question of universality of string theory.

hep-th↗