Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userParent formulations, frame-like Lagrangians, and generalized auxiliary fields
179
0
0.0
(
0
)
Authors
Maxim Grigoriev
Ask ChatGPT about the research
No Arabic abstract
We elaborate on the recently proposed Lagrangian parent formulation. In particular, we identify a natural choice of the allowed field configurations ensuring the equivalence of the parent and the starting point Lagrangians. We also analyze the structure of the generalized auxiliary fields employed in the parent formulation and establish the relationship between the parent Lagrangian and the recently proposed Lagrange structure for the unfolded dynamics. As an illustration of the parent formalism a systematic derivation of the frame-like Lagrangian for totally symmetric fields starting from the Fronsdal one is given. We also present a concise and manifestly sp(2)-symmetric form of the off-shell constraints and gauge symmetries for AdS higher spin fields at the nonlinear level.
rate research
Read More
We study the construction of the intrinsic action for PDEs equipped with the compatible presymplectic structures. In particular, we explicitly demonstrate that the intrinsic action for the standard Einstein-Hilbert gravity is the familiar first-order Palatini action. We then study the example of massive spin-2 field, where the natural presymplectic structure is not complete in the sense that the associated intrinsic action does not reproduce all the equations of motion. We explicitly relate this to the differential consequences of zeroth order in the genuine Lagrangian formulation of Fierz and Pauli. Moreover, we construct a minimal multisymplectic extension of the intrinsic action that produces all the equations of motion and argue that systems of this type can be naturally regarded as multidimensional analogs of mechanical systems with constraints.
Conventional descriptions of higher-spin fermionic gauge fields appear in two varieties: the Aragone-Deser-Vasiliev frame-like formulation and the Fang-Fronsdal metric-like formulation. We review, clarify and elaborate on some essential features of these two. For frame-like free fermions in Anti-de Sitter space, one can present a gauge-invariant Lagrangian description such that the constraints on the field and the gauge parameters mimic their flat-space counterparts. This simplifies the explicit demonstration of the equivalence of the two formulations at the free level. We comment on the subtleties that may arise in an interacting theory.
Lagrangian descriptions of irreducible and reducible integer higher-spin representations of the Poincare group subject to a Young tableaux $Y[hat{s}_1,hat{s}_2]$ with two columns are constructed within a metric-like formulation in a $d$-dimensional flat space-time on the basis of a BRST approach extending the results of [arXiv:1412.0200[hep-th]]. A Lorentz-invariant resolution of the BRST complex within both the constrained and unconstrained BRST formulations produces a gauge-invariant Lagrangian entirely in terms of the initial tensor field $Phi_{[mu]_{hat{s}_1}, [mu]_{hat{s}_2}}$ subject to $Y[hat{s}_1,hat{s}_2]$ with an additional tower of gauge parameters realizing the $(hat{s}_1-1)$-th stage of reducibility with a specific dependence on the value $(hat{s}_1-hat{s}_2)=0,1,...,hat{s}_1$. Minimal BRST--BV action is suggested, being proper solution to the master equation in the minimal sector and providing objects appropriate to construct interacting Lagrangian formulations with mixed-antisymmetric fields in a general framework.
Motivated by a recent progress in studying the duality-symmetric models of nonlinear electrodynamics, we revert to the auxiliary tensorial (bispinor) field formulation of the O(2) duality proposed by us in arXiv:hep-th/0110074, arXiv:hep-th/0303192. In this approach, the entire information about the given duality-symmetric system is encoded in the O(2) invariant interaction Lagrangian which is a function of the auxiliary fields V_{alphabeta}, bar V_{dot alphadot beta}. We extend this setting to duality-symmetric systems with higher derivatives and show that the recently employed nonlinear twisted self-duality constraints amount to the equations of motion for the auxiliary tensorial fields in our approach. Some other related issues are briefly discussed and a few instructive examples are explicitly worked out.
It is well-known that a Lagrangian induces a compatible presymplectic form on the equation manifold (stationary surface, understood as a submanifold of the respective jet-space). Given an equation manifold and a compatible presymplectic form therein, we define the first-order Lagrangian system which is formulated in terms of the intrinsic geometry of the equation manifold. It has a structure of a presymplectic AKSZ sigma model for which the equation manifold, equipped with the presymplectic form and the horizontal differential, serves as the target space. For a wide class of systems (but not all) we show that if the presymplectic structure originates from a given Lagrangian, the proposed first-order Lagrangian is equivalent to the initial one and hence the Lagrangian per se can be entirely encoded in terms of the intrinsic geometry of its stationary surface. If the compatible presymplectic structure is generic, the proposed Lagrangian is only a partial one in the sense that its stationary surface contains the initial equation manifold but does not necessarily coincide with it.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
