We present a brief overview of attempts to construct de Sitter vacua in string theory and explain how the results of this 20-year endeavor could point to the fact that string theory harbors no de S...

What if string theory has no de Sitter vacua

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d N=2 theory T[M_3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.

/pdf/fivebranes-and-3-manifold-homology-2qfe1mo766.pdf

Fivebranes and 3-manifold homology

/pdf/fivebranes-and-3-manifold-homology-41ww0nmbag.pdf

We present a brief overview of attempts to construct de Sitter vacua in string theory and explain how the results of this 20-year endeavor could point to the fact that string theory harbors no de Sitter vacua at all. Making such a statement is often considered controversial and "bad news for string theory". We discuss how perhaps the opposite can be true.

/pdf/what-if-string-theory-has-no-de-sitter-vacua-1ivtv0vooc.pdf

This is a review of exceptional field theory: a generalisation of Kaluza–Klein theory that unifies the metric and p-form gauge field degrees of freedom of supergravity into a generalised or extende...

The geometry, branes and applications of exceptional field theory

We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3-branes, we show that SU(0|N) supergroup theories are holographically dual to an exotic variant of type IIB string theory on $$ {\mathrm{dS}}_{3,2}\times {\overline{\mathrm{S}}}^5 $$
 , for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov’s instanton calculus, all of which agree, we derive the Seiberg-Witten curve for $$ \mathcal{N}=2 $$
 SU(N |M ) gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.

/pdf/negative-branes-supergroups-and-the-signature-of-spacetime-2155n1stjx.pdf

Negative Branes, Supergroups and the Signature of Spacetime

We study the realization of supergroup gauge theories using negative branes in string theory. We show that negative branes are intimately connected with the possibility of timelike compactification and exotic spacetime signatures previously studied by Hull. Isolated negative branes dynamically generate a change in spacetime signature near their worldvolumes, and are related by string dualities to a smooth M-theory geometry with closed timelike curves. Using negative D3 branes, we show that $SU(0|N)$ supergroup theories are holographically dual to an exotic variant of type IIB string theory on $dS_{3,2} \times \bar S^5$, for which the emergent dimensions are timelike. Using branes, mirror symmetry and Nekrasov's instanton calculus, all of which agree, we derive the Seiberg-Witten curve for $\mathcal N=2 ~SU(N|M)$ gauge theories. Together with our exploration of holography and string dualities for negative branes, this suggests that supergroup gauge theories may be non-perturbatively well-defined objects, though several puzzles remain.

Robbert Dijkgraaf

Papers

Negative Branes, Supergroups and the Signature of Spacetime

Negative Branes, Supergroups and the Signature of Spacetime