A Unified Approach to Standard and Exotic Dualizations Through Graded Geometry

Chatzistavrakidis, Athanasios; Karagiannis, Georgios; Schupp, Peter

doi:10.1007/s00220-020-03728-x

Cited by 11 publications

(22 citation statements)

References 64 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It would be worthwhile to compare our work with the action proposed in the interesting articles [24,25], where a very different approach is followed to derive an action for the double dual graviton field. The authors of [24,25] extend to the double dual case the parent action method used in [26] for first-dualization of the graviton, resulting in an action different from ours and containing, as here, (different) additional fields and (different) additional gauge symmetries (see also [27] for recent work on this type of actions). which is independent from the original (2, 2)-field unless one imposes a self-duality condition as in [2,28,29] (see [19] for the implementation of the self-duality condition in the action, and [30] for further considerations on dimensional reduction).…”

Section: Lagrangian For the C-fieldmentioning

confidence: 94%

A note on the double dual graviton

Henneaux

Lekeu

Leonard

2019

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

The (free) graviton admits, in addition to the standard Pauli-Fierz description by means of a ranktwo symmetric tensor, a description in which one dualizes the corresponding (2, 2)-curvature tensor on one column to get a (D − 2, 2)-tensor, where D is the spacetime dimension. This tensor derives from a gauge field with mixed Yound symmetry (D − 3, 1) called the "dual graviton" field. The dual graviton field is related non-locally to the Pauli-Fierz field (even on-shell), in much the same way as a p-form potential and its dual (D − p − 2)-form potential are related in the theory of an abelian p-form. Since the Pauli-Fierz field has a Young tableau with two columns (of one box each), one can contemplate a double dual description in which one dualizes on both columns and not just on one. The double dual curvature is now a (D − 2, D − 2)-tensor and derives from a gauge field with (D − 3, D − 3) mixed Young symmetry, the "double dual graviton" field. We show, however, that the double dual graviton field is algebraically and locally related to the original Pauli-Fierz field and, so, does not provide a truly new description of the graviton. From this point of view, it plays a very different role from the dual graviton field obtained through a single dualization. We also show that these equations can be obtained from a variational principle in which the variables to be varied in the action are (all) the components of the double-dual field as well as an auxiliary field with (2, 1) Young symmetry. By gauge fixing the shift symmetries of this action principle, one recovers the Pauli-Fierz action. Our approach differs from the interesting approach based on parent actions and covers only the free, sourceless theory. Similar results are argued to hold for higher spin gauge fields.

show abstract

Section: Lagrangian For the C-fieldmentioning

confidence: 94%

A note on the double dual graviton

Henneaux

Lekeu

Leonard

2019

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…There are two interesting choices of convention for this parity. The one we adopt in the present paper-and also in [6,7]-is ε(A, A) = 1 and ε(A, B) = 0 for A = B. This means that degree-1 coordinates across different sets are commuting.…”

Section: Multipartite Tensors In Graded Geometrymentioning

confidence: 99%

“…It is based on Refs. [6,7], where more details and references may be found. Graded geometry is based on the introduction of coordinates with different degrees, satisfying graded commutation relations.…”

Section: Introductionmentioning

confidence: 99%

“…The usefulness of graded geometry is demonstrated in the construction of universal Lagrangians that capture theories for any type of field, although their local coordinate counterparts may look rather different [6,7]. In this work we focus on single field, linear gauge theories in flat space, with higher derivative interactions leading to second order field equations so as to avoid Ostrogradski ghosts.…”

Section: Introductionmentioning

confidence: 99%

“…This paper includes two results that do not appear in [6,7]. The first is the already mentioned generalised kinetic term that unifies the kinetic and higher-derivative interacting sector of the bipartite tensor Lagrangians, see Eq.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Graded Geometry and Tensor Gauge Theories

Chatzistavrakidis¹,

Karagiannis²,

Schupp³

2020

Proceedings of Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2019)

Self Cite

View full text Add to dashboard Cite

We review the construction of Lagrangians for higher spin fields of mixed symmetry in the framework of graded geometry. The main advantage of the graded formalism in this context is that it provides universal expressions, in the sense that a given Lagrangian describes the dynamics of any type of bosonic tensor field even though the corresponding explicit expressions in terms of local field components and their derivatives look rather different. Aside from free fields and their kinetic terms, we also consider higher derivative interaction terms that lead to second order field equations. For scalars, differential forms and bipartite tensors, these are identified with Galileon theories, written in a simple yet elegant form as a generalised kinetic term, and are gauge invariant by construction. For fields of spin higher than 2, we illustrate the candidate Galileon-like interactions and argue that full gauge invariance and locality cannot be simultaneously maintained.

show abstract

Duality and Higher Buscher Rules in p‐Form Gauge Theory and Linearized Gravity

Chatzistavrakidis

Karagiannis

Ranjbar

2021

Fortschritte der Physik

Self Cite

View full text Add to dashboard Cite

We perform an in‐depth analysis of the transformation rules under duality for couplings of theories containing multiple scalars, p‐form gauge fields, linearized gravitons or (p, 1) mixed symmetry tensors. Following a similar reasoning to the derivation of the Buscher rules for string background fields under T‐duality, we show that the couplings for all classes of aforementioned multi‐field theories transform according to one of two sets of duality rules. These sets comprise the ordinary Buscher rules and their higher counterpart; this is a generic feature of multi‐field theories in spacetime dimensions where the field strength and its dual are of the same degree. Our analysis takes into account topological theta terms and generalized B‐fields, whose behavior under duality is carefully tracked. For a 1‐form or a graviton in 4D, this reduces to the inversion of the complexified coupling or generalized metric under electric/magnetic duality. Moreover, we write down an action for linearized gravity in the presence of θ‐term from which we obtain previously suggested on‐shell duality and double duality relations. This also provides an explanation for the origin of theta in the gravitational duality relations as a specific additional sector of the linearized gravity action.

show abstract

A Unified Approach to Standard and Exotic Dualizations Through Graded Geometry

Cited by 11 publications

References 64 publications

A note on the double dual graviton

A note on the double dual graviton

Graded Geometry and Tensor Gauge Theories

Duality and Higher Buscher Rules in p‐Form Gauge Theory and Linearized Gravity

Contact Info

Product

Resources

About