Higher Structures in M-Theory

The key open problem of string theory remains its non-perturbative completion to M-theory. A decisive hint to its inner workings comes from numerous appearances of higher structures in the limits of M-theory that are already understood, such as higher degree flux fields and their dualities, or the higher algebraic structures governing closed string field theory. These are all controlled by the higher homotopy theory of derived categories, generalised cohomology theories, and $L_\infty$-algebras. This is the introductory chapter to the proceedings of the LMS/EPSRC Durham Symposium on Higher Structures in M-Theory. We first review higher structures as well as their motivation in string theory and beyond. Then we list the contributions in this volume, putting them into context.Comment: 22 pages, Introductory Article to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018, references update

On the Empirical Consequences of the AdS/CFT Duality

We provide an analysis of the empirical consequences of the AdS/CFT duality with reference to the application of the duality in a fundamental theory, effective theory and instrumental context. Analysis of the first two contexts is intended to serve as a guide to the potential empirical and ontological status of gauge/gravity dualities as descriptions of actual physics at the Planck scale. The third context is directly connected to the use of AdS/CFT to describe real quark-gluon plasmas. In the latter context, we find that neither of the two duals are confirmed by the empirical data.Comment: 15 pages + abstract, references. Submitted to "Beyond Spacetime" volum

The Dimensions of Field Theory : From Particles to Strings

This is an editorial summary of the contents of a Book comprising a set of Articles by acknowledged experts dealing with the impact of Field Theory on major areas of physics (from elementary particles through condensed matter to strings), arranged subjectwise under six broad heads. The Book which emphasizes the conceptual, logical and formal aspects of the state of the art in these respective fields, carries a Foreword by Freeman Dyson, and is to be published by the Indian National Science Academy on the occasion of the International Mathematical Year 2000. The authors and full titles of all the Articles (33) are listed sequentially (in the order of their first appearance in the narration) under the bibliography at the end of this Summary, while a few of the individual articles to appear in the Book are already available on the LANL internet.Comment: LaTex file, 24 page

Spacetime and Physical Equivalence

In this essay I begin to lay out a conceptual scheme for: (i) analysing dualities as cases of theoretical equivalence; (ii) assessing when cases of theoretical equivalence are also cases of physical equivalence. The scheme is applied to gauge/gravity dualities. I expound what I argue to be their contribution to questions about: (iii) the nature of spacetime in quantum gravity; (iv) broader philosophical and physical discussions of spacetime. (i)-(ii) proceed by analysing duality through four contrasts. A duality will be a suitable isomorphism between models: and the four relevant contrasts are as follows: (a) Bare theory: a triple of states, quantities, and dynamics endowed with appropriate structures and symmetries; vs. interpreted theory: which is endowed with, in addition, a suitable pair of interpretative maps. (b) Extendable vs. unextendable theories: which can, respectively cannot, be extended as regards their domains of application. (c) External vs. internal intepretations: which are constructed, respectively, by coupling the theory to another interpreted theory vs. from within the theory itself. (d) Theoretical vs. physical equivalence: which contrasts formal equivalence with the equivalence of fully interpreted theories. I apply this scheme to answering questions (iii)-(iv) for gauge/gravity dualities. I argue that the things that are physically relevant are those that stand in a bijective correspondence under duality: the common core of the two models. I therefore conclude that most of the mathematical and physical structures that we are familiar with, in these models, are largely, though crucially never entirely, not part of that common core. Thus, the interpretation of dualities for theories of quantum gravity compels us to rethink the roles that spacetime, and many other tools in theoretical physics, play in theories of spacetime.Comment: 25 pages. Winner of the essay contest "Space and Time After Quantum Gravity" of the University of Illinois at Chicago and the University of Genev

The Rational Higher Structure of M-theory

We review how core structures of string/M-theory emerge as higher structures in super homotopy theory; namely from systematic analysis of the brane bouquet of universal invariant higher central extensions growing out of the superpoint. Since super homotopy theory is immensely rich, to start with we consider this in the rational/infinitesimal approximation which ignores torsion-subgroups in brane charges and focuses on tangent spaces of super space-time. Already at this level, super homotopy theory discovers all super $p$-brane species, their intersection laws, their M/IIA-, T- and S-duality relations, their black brane avatars at ADE-singularities, including their instanton contributions, and, last not least, Dirac charge quantization: for the D-branes it recovers twisted K-theory, rationally, but for the M-branes it gives cohomotopy cohomology theory. We close with an outlook on the lift of these results beyond the rational/infinitesimal approximation to a candidate formalization of microscopic M-theory in super homotopy theory.Comment: 32 pages, Contribution to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 201

Mirror Symmetry and Other Miracles in Superstring Theory

The dominance of string theory in the research landscape of quantum gravity physics (despite any direct experimental evidence) can, I think, be justified in a variety of ways. Here I focus on an argument from mathematical fertility, broadly similar to Hilary Putnam's 'no miracles argument' that, I argue, many string theorists in fact espouse. String theory leads to many surprising, useful, and well-confirmed mathematical 'predictions' - here I focus on mirror symmetry. These predictions are made on the basis of general physical principles entering into string theory. The success of the mathematical predictions are then seen as evidence for framework that generated them. I attempt to defend this argument, but there are nonetheless some serious objections to be faced. These objections can only be evaded at a high (philosophical) price.Comment: For submission to a Foundations of Physics special issue on "Forty Years Of String Theory: Reflecting On the Foundations" (edited by G. `t Hooft, E. Verlinde, D. Dieks and S. de Haro)