Multimetric supergravities

We study super-Chern-Simons theory on a generic supermanifold. After a self-contained review of integration on supermanifolds, the complexes of forms (superforms, pseudo-forms and integral forms) and the extended Cartan calculus are discussed. We then introduce Picture Changing Operators. We provide several examples of computation of PCO's acting on different type of forms. We illustrate also the action of the η operator, crucial ingredient to define the interactions of super Chern-Simons theory. Then, we discuss the action for super Chern-Simons theory on any supermanifold, first in the factorized form (3-form × PCO) and then, we consider the most general expression. The latter is written in term of psuedo-forms containing an infinite number of components. We show that the free equations of motion reduce to the usual Chern-Simons equations yielding the proof of the equivalence between the formulations at different pictures of the same theory. Finally, we discuss the interaction terms. They require a suitable definition in order to take into account the picture number. That implies the construction of a 2-product which is not associative that inherits an A ∞ algebra structure. That shares several similarities with a recent construction of a super string field theory action by

Section: Scs With Pseudoformsmentioning

confidence: 99%

Pictures from super Chern-Simons theory

Cremonini

Grassi

2020

“…Note that for the heterotic case, we have obtained a consistent tree-level amplitude that describes the interaction between massless and massive spin-2 particles, with 16 supercharges. It would be interesting to see whether the susy reduction of this theory is identical to the multi-metric gravity theories [28], and its N = 1 extension [29], that is known to be free of the Boulware-Deser ghost [30].…”

Section: Actionsmentioning

confidence: 99%

Factorization of chiral string amplitudes

Huang

Siegel

Yuan

2016

Abstract:We re-examine a closed-string model defined by altering the boundary conditions for one handedness of two-dimensional propagators in otherwise-standard string theory. We evaluate the amplitudes using Kawai-Lewellen-Tye factorization into openstring amplitudes. The only modification to standard string theory is effectively that the spacetime Minkowski metric changes overall sign in one open-string factor. This cancels all but a finite number of states: as found in earlier approaches, with enough supersymmetry (e.g., type II) the tree amplitudes reproduce those of the massless truncation of ordinary string theory. However, we now find for the other cases that additional fields, formerly thought to be auxiliary, describe new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic). The tachyon is always a ghost, but can be avoided in the heterotic case.

“…Applying a simple 2-site model, i.e. two vielbein e a and f a , with the discretization operator as the replacement for the y derivative, which is 14) and taking f a to be non-dynamically (by sending its Planck mass to infinity), so that f a = δ a is the Minkowski vacuum, we obtain the ghost-free, self-interacting massive gravity: 15) subject to a constraint arising from gauge-fixing…”

Section: Deconstruction and Ghost-free Self-interacting Massive Spinmentioning

confidence: 99%

“…However, the bosonic theory is not the one considered here, but rather that of [13] which nonlinearly contains ghosts. Reference [14] gives a superfield generalization of the ghost-free massive gravity Lagrangian. While this maintains local sypersymmetry, it does not necessarily ensure a vacuum with global supersymmetry, which is necessary to be viewed as an interacting theory of a single spin 2 supermultiplet.…”

Section: Introductionmentioning

confidence: 99%

Deconstructing supergravity: massive supermultiplets

Ondo

Tolley

2018

Given the success of the deconstruction program in obtaining ghost-free massive gravity from 5-D Einstein gravity, we propose a modification of the deconstruction procedure that incorporates supersymmetry at the linear level. We discuss the relevant limits of a conjectured interacting theory of a massive spin 2 supermultiplet, and determine the linear theory to be the N = 1 Zinoviev theory, a supersymmetric extension of Fierz-Pauli theory. We develop a family of 1-site deconstruction procedures for fermionic fields (yielding Dirac and Majorana mass terms). The deconstruction procedure appropriate for giving fermions a Dirac mass is found to preserve half of the supersymmetry of the 5-D theory. We explicitly check this by deconstructing 5-D N = 2 super-Maxwell theory down to 4-D N = 1 super-Proca theory, and deconstructing linear 5-D N = 2 supergravity down to 4-D N = 1 Zinoviev theory, and derive the full 4-D supersymmetry algebras and Stückelberg symmetries from the 5-D superalgebras and gauge symmetries, respectively. We conjecture that this procedure should admit a generalization to fully non-linear theories.