Negative branes, supergroups and the signature of spacetime

We propose a new vertex formalism, called anti-refined topological vertex (anti-vertex for short), to compute the generalized topological string amplitude, which gives rise to the supergroup gauge theory partition function. We show the one-to-many correspondence between the gauge theory and the Calabi-Yau geometry, which is peculiar to the supergroup theory, and the relation between the ordinary vertex formalism and the vertex/anti-vertex formalism through the analytic continuation.

Section: Building Blockmentioning

confidence: 95%

Section: Contents 1 Introductionmentioning

confidence: 99%

Topological vertex/anti-vertex and supergroup gauge theory

Kimura

Sugimoto

2020

“…At the point in such a solution whereH = 0 there is a naked spacetime singularity. However, certain brane probes do not see this singularity and as a result it has been argued that one can attempt to make some sense of them in string theory [46]. For example, a doubled string in the negative F1 background has generalised metric and dilaton…”

Section: Exploring Newton-cartan Backgrounds In Doubled Geometrymentioning

confidence: 99%

“…At the pointH = 0, the bottom right block of the generalised metric is non-invertible, and the generalised metric is exactly of the type (1, 1) form that describes the Newton-Cartan geometry we have studied in this paper. This is therefore a background in which forH > 0 andH < 0 we have strings probing a relativistic geometry (however with different potentially "exotic" variants of string theory in each region, possibly with different signatures of spacetime [46]), while at the naively singular regionH = 0 in spacetime the string theory sees a non-relativistic background.…”

Section: Exploring Newton-cartan Backgrounds In Doubled Geometrymentioning

confidence: 99%

A worldsheet supersymmetric Newton-Cartan string

Blair

2019

We construct a (locally) supersymmetric worldsheet action for a string in a non-relativistic Newton-Cartan background. We do this using a doubled string action, which describes the target space geometry in an O(D, D) covariant manner using a doubled metric and doubled vielbeins. By adopting different parametrisations of these doubled background fields, we can describe both relativistic and non-relativistic geometries. We focus on the torsional Newton-Cartan geometry which can be obtained by null duality/reduction (such null duality is particularly simple for us to implement). The doubled action we use gives the Hamiltonian form of the supersymmetric Newton-Cartan string action automatically, from which we then obtain the equivalent Lagrangian. We extract geometric quantities of interest from the worldsheet couplings and write down the supersymmetry transformations. Our general results should apply to other non-relativistic backgrounds. We comment on the usefulness of the doubled approach as a tool for studying non-relativistic string theory.

“…The analysis can be extended to other hidden symmetry algebras [15]. Multiple time physics has a long history (for a survey of two-time physics, see [16]) and has recently been shown to be connected with supergroup gauge theories and negative branes [17].…”

Section: Introductionmentioning

confidence: 99%

Timelike duality, M′-theory and an exotic form of the Englert solution

Henneaux

Ranjbar

2017

Through timelike dualities, one can generate exotic versions of M -theory with different spacetime signatures. These are the M * -theory with signature (9, 2, −), the M ′ -theory, with signature (6, 5, +) and the theories with reversed signatures (1, 10, −), (2, 9, +) and (5, 6, −). In (s, t, ±), s is the number of space directions, t the number of time directions, and ± refers to the sign of the kinetic term of the 3 form.The only irreducible pseudo-riemannian manifolds admitting absolute parallelism are, besides Lie groups, the seven-sphere S 7 ≡ SO(8)/SO(7) and its pseudo-riemannian version S 3,4 ≡ SO(4, 4)/SO(3, 4). [There is also the complexification SO(8, C)/SO(7, C), but it is of dimension too high for our considerations.] The seven-sphere S 7 ≡ S 7,0 has been found to play an important role in 11-dimensional supergravity, both through the Freund-Rubin solution and the Englert solution that uses its remarkable parallelizability to turn on non trivial internal fluxes. The spacetime manifold is in both cases AdS 4 ×S 7 . We show that S 3,4 enjoys a similar role in M ′ -theory and construct the exotic form AdS 4 ×S 3,4 of the Englert solution, with non zero internal fluxes turned on. There is no analogous solution in M * -theory.