Dual projection and self-duality in three dimensions

Banerjee, Rabin; Wotzasek, C.

doi:10.1103/physrevd.63.045005

Cited by 15 publications

(35 citation statements)

References 16 publications

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“…This has also been discussed in another contexts [19,9]. As we have pointed in relation to equation (5) in the Introduction, HD in (2+1)-dimensions is ill defined unless we use doublets of different tensor rank as we show below; otherwise, we only can work merely with the already known DHD described in the introduction by the action (2).…”

Section: (2+1)-dimensions: Maxwell Theory and Manifest Hdmentioning

confidence: 85%

Hodge-type self(antiself)-duality for general p-form fields in arbitrary dimensions

Cantcheff

2002

EPJ direct

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It is often claimed [1] that the (Hodge type) duality operation is defined only in even dimensional spacetimes and that self-duality is further restricted to twice-odd dimensional spacetime theories. The purpose of this paper is to extend the notion of both duality symmetry as well as self-duality.By considering tensorial doublets, we introduce a novel well-defined notion of self-duality based on a duality Hodge-type operation in arbitrary dimension and for any rank of these tensors. Thus, a generalized Self-Dual Action is defined such that equations of motion are the claimed generalized self-duality relations. We observe in addition, that taking the proper limit on the parameters of this action, it always provides us with a master-action, which interpolates models well-studied in physics; by considering a particular limit, we find an action which describes an interesting type of relation, referred to as semi-self-duality, which results to be the parent action between Maxwell-type actions.Finally, we apply these ideas to construct manifest Hodge-type self-dual solutions in a (2+1)-dimensional version of the Maxwell's theory.

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Section: (2+1)-dimensions: Maxwell Theory and Manifest Hdmentioning

confidence: 85%

Hodge-type self(antiself)-duality for general p-form fields in arbitrary dimensions

Cantcheff

2002

EPJ direct

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“…In fact I here follow [20] to show that the construction of an internal space is useful in this context and that a discrete Z 2 symmetry can appear. I start by following [20] with an example of even-dimensional (2n) electrodynamics. Let A be a general (n − 1) form and F k 1 ...k n its associated field strength:…”

Section: Internal Spaces and Dualitymentioning

confidence: 99%

A Field-Theoretical Approach to the P vs. NP Problem via the Phase Sign of Quantum Monte Carlo

Patrascu

2017

Condensed Matter

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I present here a new method that allows the introduction of a discrete auxiliary symmetry in a theory in such a way that the eigenvalue spectrum of the fermion functional determinant is made up of complex conjugated pairs. The method implies a particular way of introducing and integrating over auxiliary fields related to a set of artificial shift symmetries. Gauge fixing the artificial continuous shift symmetries in the direct and dual sectors leads to the appearance of direct and dual Becchi-Rouet-Stora-Tyutin (BRST)-type global symmetries and of a symplectic structure over the field space. Such a method may allow the extension of the applicability of quantum Monte Carlo methods to some problems plagued by the fermionic sign problem.

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“…We are seeking for a dual description in which the deformed momentum brackets (19) are mapped to the field space deformed ones (20). The relevant relation is then…”

Section: The Dual Formulationmentioning

confidence: 99%

“…We shall adopt the O(2) decomposition, instead of the usual textbook U(1), given by (for details see [19,20]). …”

Section: The Dual Formulationmentioning

confidence: 99%

Induced deformation of the canonical structure and UV/IR duality in(1+1)D

2008

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The purpose of this work is two fold. Working in the framework of (1 + 1)D Lorentz violating field theories we will investigate in the first place the general claim that fermionic interactions may be equivalent to a deformation of the canonical structure of the theory. Second the deformed theory will be studied using duality reasoning to address the behavior of the Infra-Red and Ultra-Violet regimes.

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Dual projection and self-duality in three dimensions

Cited by 15 publications

References 16 publications

Hodge-type self(antiself)-duality for general p-form fields in arbitrary dimensions

Hodge-type self(antiself)-duality for general p-form fields in arbitrary dimensions

A Field-Theoretical Approach to the P vs. NP Problem via the Phase Sign of Quantum Monte Carlo

Induced deformation of the canonical structure and UV/IR duality in(1+1)D

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