Ground states of duality-twisted sigma-models with K 3 target space

Ganor, Ori; Jue, Sharon; McCurdy, Shannon R.

doi:10.1007/jhep02(2013)017

Cited by 3 publications

(3 citation statements)

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“…The idea of T-folds can be naturally extended to compactifications with S-duality twists (i.e. twisting by a symmetry of the equations of motion [105] ) or U-duality twists (U-folds) [6,7,106] and, given the understanding of mirror symmetry as T-duality [107], may allow mirror-folds for Calabi-Yau compactifications as first suggested in [6] (this concept has been studied in the context of K3 target spaces in [108,109,110]).…”

Section: T-foldsmentioning

confidence: 99%

Duality symmetric string and M-theory

2015

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We review recent developments in duality symmetric string theory. We begin with the worldsheet doubled formalism which describes strings in an extended spacetime with extra coordinates conjugate to winding modes. This formalism is T-duality symmetric and can accommodate non-geometric T-fold backgrounds which are beyond the scope of Riemannian geometry. Vanishing of the conformal anomaly of this theory can be interpreted as a set of spacetime equations for the background fields. These equations follow from an action principle that has been dubbed Double Field Theory (DFT). We review the aspects of generalised geometry relevant for DFT. We outline recent extensions of DFT and explain how, by relaxing the so-called strong constraint with a Scherk-Schwarz ansatz, one can obtain backgrounds that simultaneously depend on both the regular and T-dual coordinates. This provides a purely geometric higher dimensional origin to gauged supergravities that arise from non-geometric compactification. We then turn to M-theory and describe recent progress in formulating an E n(n) U-duality covariant description of the dynamics. We describe how spacetime may be extended to accommodate coordinates conjugate to brane wrapping modes and the construction of generalised metrics in this extended space that unite the bosonic fields of supergravity into a single object. We review the action principles for these theories and their novel gauge symmetries. We also describe how a Scherk-Schwarz reduction can be applied in the M-theory context and the resulting relationship to the embedding tensor formulation of maximal gauged supergravities.

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Section: T-foldsmentioning

confidence: 99%

Duality symmetric string and M-theory

2015

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“…which easily follows from 2G = E + E t . Quantum mechanically, the boundary conditions (4.13) are introduced by inserting a "duality wall" (see for instance [39] and the supersymmetric case discussed in [40]). The T-duality wall can be thought of as the dimensional reduction of the T (U(1)) theory, 5 and in general, to incorporate the M twist into the action we have to decompose M in terms of the generators…”

Section: T-duality Twistmentioning

confidence: 99%

Double-Janus linear sigma models and generalized reciprocity for Gauss sums

Ganor

Sun

Torres-Chicon

2021

J. High Energ. Phys.

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We study the supersymmetric partition function of a 2d linear σ-model whose target space is a torus with a complex structure that varies along one worldsheet direction and a Kähler modulus that varies along the other. This setup is inspired by the dimensional reduction of a Janus configuration of 4d $$ \mathcal{N} $$ N = 4 U(1) Super-Yang-Mills theory compactified on a mapping torus (T2 fibered over S1) times a circle with an SL(2, ℤ) duality wall inserted on S1, but our setup has minimal supersymmetry. The partition function depends on two independent elements of SL(2, ℤ), one describing the duality twist, and the other describing the geometry of the mapping torus. It is topological and can be written as a multivariate quadratic Gauss sum. By calculating the partition function in two different ways, we obtain identities relating different quadratic Gauss sums, generalizing the Landsberg-Schaar relation. These identities are a subset of a collection of identities discovered by F. Deloup. Each identity contains a phase which is an eighth root of unity, and we show how it arises as a Berry phase in the supersymmetric Janus-like configuration. Supersymmetry requires the complex structure to vary along a semicircle in the upper half-plane, as shown by Gaiotto and Witten in a related context, and that semicircle plays an important role in reproducing the correct Berry phase.

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“…Orbifolding by T-duality offers a manageable class of non-geometric backgrounds that are more clearly understood from the viewpoint of orbifold constructions. More broadly speaking, the automorphism group can be non-perturbative when we twist boundary conditions by S-duality (see for example [12,13,14,15]) or more generally Uduality [16,17,18]. Understanding these stringy monodrofolds [19] is not only interesting in its own right, but they may also have some implications for string cosmology [20,21,22,23], string phenomenology [24,25,26] and modern duality-covariant frameworks of string theory such as the likes of 'Double Field Theory' (see for example [27]) and gauged supergravity theories [28,29,30].…”

Section: Introductionmentioning

confidence: 99%

T-duality twists and asymmetric orbifolds

Tan

2015

J. High Energ. Phys.

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Abstract:We study some aspects of asymmetric orbifolds of tori, with the orbifold group being some Z N subgroup of the T-duality group and, in particular, provide a concrete understanding of certain phase factors that may accompany the T-duality operation on the stringy Hilbert space in toroidal compactification. We discuss how these T-duality twist phase factors are related to the symmetry and locality properties of the closed string vertex operator algebra, and clarify the role that they enact in the modular covariance of the orbifold theory, mainly using asymmetric orbifolds of tori which are root lattices as working examples.

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Ground states of duality-twisted sigma-models with K 3 target space

Cited by 3 publications

References 50 publications

Duality symmetric string and M-theory

Duality symmetric string and M-theory

Double-Janus linear sigma models and generalized reciprocity for Gauss sums

T-duality twists and asymmetric orbifolds

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