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The purpose of this paper is to make the theory of vertex algebras trivial. We do this by setting up some categorical machinery so that vertex algebras are just ``singular commutative rings'' in a certain category. This makes it easy to…
The notion of (symmetric) coloured operad or "multicategory" can be obtained from the notion of commutative algebra through a certain general process which we call "theorization" (where our term comes from an analogy with William Lawvere's…
A careful treatment of closed string BRST cohomology shows that there are more discrete states and associated symmetries in $D=2$ string theory than has been recognized hitherto. The full structure, at the $SU(2)$ radius, has a natural…
In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical…
It has been suggested that reality works like a quantum computer, but such claims are just words if they are not backed up by sound mathematics. In pursuit of the fundamental equations I look to string theory where physicists led by Mike…
A series of successive quantizations is considered, starting with the quantization of a non relativistic or relativistic point particle: 1) quantization of a particle's position, 2) quantization of wave function, 3) quantization of wave…
The purely mathematical root of the dequantization constructions is the quest for a sheafification needed for presheaves on a noncommutative space. The moment space is constructed as a commutative space, approximating the noncommutative…
I describe our understanding of physics near the planck length, in particular the great progress of the last four years in string theory. Superstring theory, and a recent extension called M theory, are leading candidates for a quantum…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
We argue that in the tensionless phase of string theory where the stringy gauge symmetries are unbroken, (at least some) cosmological singularities can be understood as gauge artefacts. We present two conceptually related, but distinct,…
A virtual string is a scheme of self-intersections of a closed curve on a surface. We study algebraic invariants of strings as well as two equivalence relations on the set of strings: homotopy and cobordism. We show that the homotopy…
String theory provides the only consistent framework so far that unifies all interactions including gravity. We discuss gravity and cosmology in string theory. Conventional notions from general relativity like geometry, topology etc. are…
The paper is devoted to a description of quantum group structures in the geometric quantization of a self-interacting string field, which appear under a transition from a tree-level of the theory to the account of loop effects in…
In a natural extension of the relativity principle we argue that a quantum theory of gravity involves two fundamental scales associated with both dynamical space-time as well as dynamical momentum space. This view of quantum gravity is…
We examine various properties of double field theory and the doubled string sigma model in the context of geometric quantisation. In particular we look at T-duality as the symplectic transformation related to an alternative choice of…
String theory has been the dominating research field in theoretical physics during the last decades. Despite the considerable time elapse, no new testable predictions have been derived by string theorists and it is understandable that…
String Theory is the result of the conjunction of three conceptually independent elements: (i) the metaphysical idea of a nomological unity of the forces, (ii) the model-theoretical paradigm of Quantum Field Theory, and (iii) the conflict…
In this work we extend the notion of co-algebra, co-algebraic Wess-Zumino-Witten formulation of Lagrangian Field Theory and the Homotopy transfer theorem to many strings and particle systems. We discuss in detail the construction of higher…
We study the canonical quantization of a bosonic string in presence of N twist fields. This generalizes the quantization of the twisted string in two ways: the in and out states are not necessarily twisted and the number of twist fields N…
The status of string theory is reviewed, and major recent developments - especially those in going beyond perturbation theory in the string theory and quantum field theory frameworks - are discussed. This analysis helps better understand…