Scalar potential for the gauged Heisenberg algebra and a non-polynomial antisymmetric tensor theory (original) (raw)

Non-Abelian tensor gauge fields and extended current algebra

We suggest an infinite-dimensional extension of the gauge transformations which includes non-Abelian tensor gauge fields. Extended gauge transformations of non-Abelian tensor gauge fields form a new large group which has natural geometrical interpretation it terms of extended current algebra associated with compact Lie group. We shall demonstrate that one can construct two infinite series of gauge invariant quadratic forms, so that a linear combination of them comprises the general Lagrangian. The general Lagrangian exhibits enhanced local gauge invariants with double number of gauge parameters and allows to eliminate all negative norm states of the nonsymmetric second-rank tensor gauge field. Therefore it describes two polarizations of helicity-two and helicity-zero massless charged tensor gauge bosons.

Non-Abelian tensor gauge fields and extended current algebra. Generalization of Yang-Mills theory

The gauge structure of exceptional field theories and the tensor hierarchy

Journal of High Energy Physics, 2014

ABSTRACT We address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying structure, compatible with E_{11} and Borcherds algebras constructions. We begin with four-dimensional gauged maximal supergravity, and build a generalized Lie derivative that encodes all the gauge transformations of the theory. A generalized frame is introduced, which accommodates for all the degrees of freedom, including the tensor hierarchy. The generalized Lie derivative defines generalized field-dependent fluxes containing all the covariant quantities in the theory, and the closure conditions give rise to their corresponding Bianchi Identities. We then move towards the construction of a full generalized Lie derivative defined on an extended space, analyze the closure conditions, and explore the connection with that of maximal gauged supergravity via a generalized Scherk-Schwarz reduction, and with 11-dimensional supergravity.

Standard Models from Heterotic M-theory

Advances in Theoretical and Mathematical Physics

We present a class of N = 1 supersymmetric models of particle physics, derived directly from heterotic M-theory, that contain three families of chiral quarks and leptons coupled to the gauge group SU (3) C ×SU (2) L ×U (1) Y . These models are a fundamental form of "brane-world" theories, with an observable and hidden sector each confined, after compactification on a Calabi-Yau threefold, to a BPS three-brane separated by a five dimensional bulk space with size of the order of the intermediate scale. The requirement of three families, coupled to the fundamental conditions of anomaly freedom and supersymmetry, constrains these models to contain additional five-branes wrapped around holomorphic curves in the Calabi-Yau threefold. These five-branes "live" in the bulk space and represent new, non-perturbative aspects of these particle physics vacua. We discuss, in detail, the relevant mathematical structure of a class of torusfibered Calabi-Yau threefolds with non-trivial first homotopy groups and construct holomorphic vector bundles over such threefolds, which, by including Wilson lines, break the gauge symmetry to the standard model gauge group. Rules for constructing phenomenological particle physics models in this context are presented and we give a number of explicit examples.

Flux compactifications of Type II string theories under non-perturbative dualities

2010

We consider string vacua formed by compactifying Type II string theories on toroidal orbifolds and generalised Calabi-Yau manifolds and their transformations under a set of non-perturbative dualities. The dualities are the Type IIA-IIB exchanging T duality, the self-symmetry of Type IIB S duality, the non-trivial combination of the two, U duality, and the generalisation of T duality to include Calabi-Yaus, mirror symmetry. The requirement of the effective theory superpotential being invariant under these dualities is used to justify additional fluxes which do not descend via compactification from the ten dimensional action, which form an N = 2 theory. Their non-geometric structures, Bianchi constraints and tadpoles are determined and then classified in terms of modular S duality induced multiplets. The Z2 Z2 orientifold is used as an explicit example of the general methods, with N = 1 Type IIB non-geometric vacua which possess T and S duality invariance also constructed. These are t...

Noncommutative gauge theories on R2θ as matrix models

2016

We study a class of noncommutative gauge theory models on 2-dimensional Moyal space from the viewpoint of matrix models and explore some related properties. Ex-panding the action around symmetric vacua generates non local matrix models with polynomial interaction terms. For a particular vacuum, we can invert the kinetic oper-ator which is related to a Jacobi operator. The resulting propagator can be expressed in terms of Chebyschev polynomials of second kind. We show that non vanishing cor-relations exist at large separations. General considerations on the kinetic operators stemming from the other class of symmetric vacua, indicate that only one class of symmetric vacua should lead to fast decaying propagators. The quantum stability of the vacuum is briefly discussed.

Canonical Observables versus the Algebra of Invariant Charges for the Open Nambu String

The relationship between the canonical observables and the Pohlmeyer-Rehren infinite-dimensional tensor algebra of invariant charges is analysed for the open Nambu string. In two recent papers[1,2] the classical Nambu string has been studied by means of the many-time approach. The original pair of first-class constraints, which are only in weak involution, have been locally replaced by two sets of strictly abelian (i.e. in involution under Poisson brackets) constraints by multiplying them by suitable functions suggested by the light-cone coordinates. In this way it is possible to describe nearly all the constraint manifold using two overlapping charts, one with P + = 0, the other with P − = 0. The remaining part of such a manifold contains only longitudinal modes. In each chart the Hamilton-Dirac equations of motion are replaced by many-time functional Hamilton equations with the abelian constraints as Hamiltonians. These equations have been solved in an arbitrary gauge. Moreover a complete set of canonical observables,à la Dirac, has ben found for each chart; this set reduce to the DDF oscillators[3] in the orthonormal gauge. This allows the construction of a canonical transformation, in each chart, from the original symplectic basis x µ (σ), P µ (σ), to a new one which is made of: 1) the abelian constraints and the conjugated gauge variables; 2) all the previous transverse canonical observables; 3) the three independent components (in four space-time dimension) of the total momentum and the three conjugated variables for the center of mass (which are Dirac observables too).

Standard Model Vacua in Heterotic M-Theory

We present a class of N = 1 supersymmetric "standard" models of particle physics, derived directly from heterotic M-theory, that contain three families of chiral quarks and leptons coupled to the gauge group SU (3) C × SU (2) L × U (1) Y . These models are a fundamental form of "brane world" theories, with an observable and hidden sector each confined, after compactification on a Calabi-Yau threefold, to a BPS three-brane separated by a higher dimensional bulk space with size of the order of the intermediate scale. The requirement of three families, coupled to the fundamental conditions of anomaly freedom and supersymmetry, constrains these models to contain additional five-branes located in the bulk space and wrapped around holomorphic curves in the Calabi-Yau threefold.

IPhT-T13/227 The gauge structure of Exceptional Field Theories and the tensor hierarchy

2016

We address the construction of manifest U-duality invariant generalized diffeomorphisms. The closure of the algebra requires an extension of the tangent space to include a tensor hierarchy indicating the existence of an underlying unifying structure, compatible with E 11 and Borcherds algebras constructions. We begin with four-dimensional gauged maximal supergravity, and build a generalized Lie derivative that encodes all the gauge transformations of the theory. A generalized frame is introduced, which accommodates for all the degrees of freedom, including the tensor hierarchy. The generalized Lie derivative defines generalized field-dependent fluxes containing all the covariant quantities in the theory, and the closure conditions give rise to their corresponding Bianchi Identities. We then move towards the construction of a full generalized Lie derivative defined on an extended space, analyze the closure conditions, and explore the connection with that of maximal gauged supergravity via a generalized Scherk-Schwarz reduction, and with 11-dimensional supergravity.

Scalar potential for the gauged Heisenberg algebra and a non-polynomial antisymmetric tensor theory (original) (raw)

Related papers