Quantum mechanics of the doubled torus

Hackett-Jones, Emily J.; Moutsopoulos, George

doi:10.1088/1126-6708/2006/10/062

Cited by 33 publications

(56 citation statements)

References 29 publications

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“…(This is what is used in [22,35] in an alternative approach to the worldsheet supersymmetric doubled string.) The definition of the generalised metric in (2.7) implies the existence of projectors:…”

Section: Doubled Vielbeinsmentioning

confidence: 99%

A worldsheet supersymmetric Newton-Cartan string

Blair

2019

J. High Energ. Phys.

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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.

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Section: Doubled Vielbeinsmentioning

confidence: 99%

A worldsheet supersymmetric Newton-Cartan string

Blair

2019

J. High Energ. Phys.

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“…Demonstrating the classical equivalence of this formalism to the usual sigma model is straightforward, however, showing quantum equivalence is less trivial. This has been discussed in [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Background field equations for the duality symmetric string

2008

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This paper describes the background field equations for strings in T-duality symmetric formalisms in which the dimension of target space is doubled and the sigma model supplemented with constraints. These are calculated by demanding the vanishing of the beta-functional of the sigma model couplings in the doubled target space. We demonstrate the equivalence with the background field equations of the standard string sigma model.

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“…There are several arguments for why non-geometric configurations like those just described should be consistent backgrounds of (at least classical) string theory [33] (see [34,35,36,37,38] for related discussions on the quantized string). The string conformal field theory (CFT) should remain the same under string symmetries, even if its representation as a sigma model in terms of target space fields could change (e.g.…”

Section: Non-geometry In Various Dimensionsmentioning

confidence: 99%

“…The idea of the doubled geometry has then been used in several descriptions of non-geometry, along the lines of [54,53] for target space descriptions, and of [33,34,35] for sigma models.…”

Section: Non-geometry In Various Dimensionsmentioning

confidence: 99%

“…The top line is the proposal we make: since our change of variables from the hatted to the tilded basis leaves the generalized metric H and ∆ invariant (see (1.3), (3.10)), one should consider the DFT Lagrangian given in (4.35), but where H and ∆ are expressed in terms of the tilded variablesg,β,φ. 34 This Lagrangian (in the top-right corner of (4.37)) should provide an interesting DFT description of non-geometry, up to global issues that we discussed in section 4.1. In addition, the chain of equalities in (4.37) shows that the Lagrangians in the last column should be equal, up to a total derivative term, once one considers ∂ y = 0.…”

Section: Double Field Theory and Non-geometrymentioning

confidence: 99%

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A ten-dimensional action for non-geometric fluxes

Patalong¹

2012

Proceedings of Proceedings of the Corfu Summer Institute 2011 — PoS(CORFU2011)

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The NSNS Lagrangian of ten-dimensional supergravity is rewritten via a change of field variables inspired by Generalized Complex Geometry. We obtain a new metric and dilaton, together with an antisymmetric bivector field which leads to a ten-dimensional version of the non-geometric Q-flux. Given the involved global aspects of non-geometric situations, we prescribe to use this new Lagrangian, whose associated action is well-defined in some examples investigated here. This allows us to perform a standard dimensional reduction and to recover the usual contribution of the Q-flux to the four-dimensional scalar potential. An extension of this work to include the R-flux is discussed. The paper also contains a brief review on non-geometry.

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Quantum mechanics of the doubled torus

Cited by 33 publications

References 29 publications

A worldsheet supersymmetric Newton-Cartan string

A worldsheet supersymmetric Newton-Cartan string

Background field equations for the duality symmetric string

A ten-dimensional action for non-geometric fluxes

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