Transverse generalized metrics and 2d sigma models

Ševera, Pavol; Strobl, Thomas

doi:10.1016/j.geomphys.2019.103509

Cited by 8 publications

(9 citation statements)

References 11 publications

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“…Indeed one can show that an exact H-twisted Courant algebroid E over a manifold M is equivalent to specifying the phase space of a two-dimensional sigma-model where the Kalb-Ramond field has curvature H, see e.g. [58]. Schematically we now have a Fourier-Mukai-like diagram transporting D-branes and defects as Dirac structure from one Courant algebroid to the other…”

Section: Jhep11(2022)165mentioning

confidence: 99%

Poisson-Lie T-duality defects and target space fusion

Demulder

Raml

2022

J. High Energ. Phys.

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Topological defects have long been known to encode symmetries and dualities between physical systems. In the context of string theory, defects have been intensively studied at the level of the worldsheet. Although marked by a number of pioneering milestones, the target space picture of defects is much less understood. In this paper, we show, at the level of the target space, that Poisson-Lie T-duality can be encoded as a topological defect. With this result at hand, we can postulate the kernel capturing the Fourier-Mukai transform associated to the action of Poisson-Lie T-duality on the RR-sector. Topological defects have the remarkable property that they can be fused together or, alternatively, with worldsheet boundary conditions. We study how fusion of the proposed generalised T-duality topological defect consistently leads to the known duality transformations for boundary conditions. Finally, taking a step back from generalised T-duality, we tackle the general problem of understanding the effect of fusion at the level of the target space. We propose to use the framework of Dirac geometry and formulate the fusion of topological defects and D-branes in this language.

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Section: Jhep11(2022)165mentioning

confidence: 99%

Poisson-Lie T-duality defects and target space fusion

Demulder

Raml

2022

J. High Energ. Phys.

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“…In the following, we use this fact to absorb the 2D topological term of (2.1) in the Wess-Zumino term and therefore B µν will not appear in our analysis explicitly, but only through exact contributions stemming from H. Thus, essentially the background fields of the theory are (g, H), in other words a generalised metric, see e.g. [18].…”

Section: Dirac Sigma Models As 2d Gauge Theorymentioning

confidence: 99%

Topological Dirac sigma models and the classical master equation

Chatzistavrakidis¹,

Jonke²,

Strobl³

et al. 2023

J. Phys. A: Math. Theor.

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We present the construction of the classical Batalin-Vilkovisky action for topological Dirac sigma models. The latter are two-dimensional topological ﬁeld theories that simultaneously generalise the completely gauged Wess-Zumino-Novikov-Witten model and the Poisson sigma model. Their underlying structure is that of Dirac manifolds associated to maximal isotropic and integrable subbundles of an exact Courant algebroid twisted by a 3-form. In contrast to the Poisson sigma model, the AKSZ construction is not applicable for the general Dirac sigma model. We therefore follow a direct approach for determining a suitable BV extension of the classical action functional with ghosts and antiﬁelds satisfying the classical master equation. Special attention is paid on target space covariance, which requires the introduction of two connections with torsion on the Dirac structure.

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“…This tells us that the global symmetries of the theory are isometries of the target space geometry specified by G and H (a generalized metric in the language of [28]), and ρ a is thus a host of Killing vector fields. Another way to think about this is to rewrite (38) as…”

Section: Multiple Fields Target Space Geometry and Jetsmentioning

confidence: 99%

Duality, Generalized Global Symmetries and Jet Space Isometries

2021

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We revisit universal features of duality in linear and nonlinear relativistic scalar and Abelian 1-form theories with single or multiple fields, which exhibit ordinary or generalized global symmetries. We show that such global symmetries can be interpreted as generalized Killing isometries on a suitable, possibly graded, target space of fields or its jet space when the theory contains higher derivatives. This is realized via a generalized sigma model perspective motivated from the fact that higher spin particles can be Nambu–Goldstone bosons of spontaneously broken generalized global symmetries. We work out in detail the 2D examples of a compact scalar and the massless Heisenberg pion fireball model and the 4D examples of Maxwell, Born–Infeld, and ModMax electrodynamics. In all cases we identify the ’t Hooft anomaly that obstructs the simultaneous gauging of both global symmetries and confirm the anomaly matching under duality. These results readily generalize to higher gauge theories for p-forms. For multifield theories, we discuss the transformation of couplings under duality as two sets of Buscher rules for even or odd differential forms.

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Transverse generalized metrics and 2d sigma models

Cited by 8 publications

References 11 publications

Poisson-Lie T-duality defects and target space fusion

Poisson-Lie T-duality defects and target space fusion

Topological Dirac sigma models and the classical master equation

Duality, Generalized Global Symmetries and Jet Space Isometries

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