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Bruno Zumino

Publications and source records attributed to Bruno Zumino.

At least 19 recordsLinked to original sources
arXiv2013

Freudenthal Gauge Theory

We present a novel gauge field theory, based on the Freudenthal Triple System (FTS), a ternary algebra with mixed symmetry (not completely symmetric) structure constants. The theory, named Freudenthal Gauge Theory (FGT), is invariant under two (off-shell) symmetries: the gauge Lie algebra constructed from the FTS triple product and a novel global non-polynomial symmetry, the so-called Freudenthal duality. Interestingly, a broad class of FGT gauge algebras is provided by the Lie algebras "of type e7" which occur as conformal symmetries of Euclidean Jordan algebras of rank 3, and as U-duality algebras of the corresponding (super)gravity theories in D = 4. We prove a No-Go Theorem, stating the incompatibility of the invariance under Freudenthal duality and the coupling to space-time vector and/or spinor fields, thus forbidding non-trivial supersymmetric extensions of FGT. We also briefly discuss the relation between FTS and the triple systems occurring in BLG-type theories, in particular focusing on superconformal Chern-Simons-matter gauge theories in D = 3.

hep-th↗
arXiv2013

Jordan Pairs, E6 and U-Duality in Five Dimensions

By exploiting the Jordan pair structure of U-duality Lie algebras in D = 3 and the relation to the super-Ehlers symmetry in D = 5, we elucidate the massless multiplet structure of the spectrum of a broad class of D = 5 supergravity theories. Both simple and semi-simple, Euclidean rank-3 Jordan algebras are considered. Theories sharing the same bosonic sector but with different supersymmetrizations are also analyzed.

math-ph↗
arXiv2010

Charge Orbits of Extremal Black Holes in Five Dimensional Supergravity

We derive the U-duality charge orbits, as well as the related moduli spaces, of "large" and "small" extremal black holes in non-maximal ungauged Maxwell-Einstein supergravities with symmetric scalar manifolds in d=5 space-time dimensions. The stabilizer groups of the various classes of orbits are obtained by determining and solving suitable U-invariant sets of constraints, both in "bare" and "dressed" charges bases, with various methods. After a general treatment of attractors in real special geometry (also considering non-symmetric cases), the N=2 "magic" theories, as well as the N=2 Jordan symmetric sequence, are analyzed in detail. Finally, the half-maximal (N=4) matter-coupled supergravity is also studied in this context.

hep-th↗
arXiv2009

Covariant Star Product for Exterior Differential Forms on Symplectic Manifolds

After a brief description of the $\mathbb{Z}$-graded differential Poisson algebra, we introduce a covariant star product for exterior differential forms and give an explicit expression for it up to second order in the deformation parameter $\hbar$, in the case of symplectic manifolds. The graded differential Poisson algebra endows the manifold with a connection, not necessarily torsion-free, and places upon the connection various constraints.

hep-th↗
arXiv2009

Duality, Entropy and ADM Mass in Supergravity

We consider the Bekenstein-Hawking entropy-area formula in four dimensional extended ungauged supergravity and its electric-magnetic duality property. Symmetries of both "large" and "small" extremal black holes are considered, as well as the ADM mass formula for N=4 and N=8 supergravity, preserving different fraction of supersymmetry. The interplay between BPS conditions and duality properties is an important aspect of this investigation.

hep-th↗
arXiv2008

Duality Rotations in Nonlinear Electrodynamics and in Extended Supergravity

We review the general theory of duality rotations which, in four dimensions, exchange electric with magnetic fields. Necessary and sufficient conditions in order for a theory to have duality symmetry are established. A nontrivial example is Born-Infeld theory with n abelian gauge fields and with Sp(2n,R) self-duality. We then review duality symmetry in supergravity theories. In the case of N=2 supergravity duality rotations are in general not a symmetry of the theory but a key ingredient in order to formulate the theory itself. This is due to the beautiful relation between the geometry of special Kaehler manifolds and duality rotations.

hep-th↗
arXiv2008

Supersymmetry and Superstring Phenomenology

We briefly cover the early history of supersymmetry, describe the relation of SUSY quantum field theories to superstring theories and explain why they are considered a likely tool to describe the phenomenology of high energy particle theory beyond the Standard Model.

hep-th↗
arXiv2005

Supersymmetry then and now

A brief description of some salient aspects of four-dimensional supersymmetry: early history, supermanifolds, the MSSM, cold dark matter, the cosmological constant and the string landscape.

hep-th↗
arXiv2004

Constraints and Superspin for SuperPoincare Algebras in Diverse Dimensions

We generalize to arbitrary dimension the construction of a covariant and supersymmetric constraint for the massless superPoincare algebra, which was given for the eleven-dimensional case in a previous work. We also contrast it with a similar construction appropriate to the massive case. Finally we show that the constraint uniquely fixes the representation of the algebra.

hep-th↗
arXiv2004

Constraints and Casimirs for Superpoincare and Supertranslation Algebras in various dimensions

We describe, for arbitrary dimensions the construction of a covariant and supersymmetric constraint for the massless Super Poincare' algebra and we show that the constraint fixes uniquely the representation of the algebra. For the case of finite mass and in the absence of central charges we discuss a similar construction, which generalizes to arbitrary dimensions the concept of the superspin Casimir. Finally we discuss briefly the modifications introduced by central charges, both scalar and tensorial.

hep-th↗
arXiv2003

A Hidden Twelve-Dimensional SuperPoincare Symmetry In Eleven Dimensions

First, we review a result in our previous paper, of how a ten-dimensional superparticle, taken off-shell, has a hidden eleven-dimensional superPoincare symmetry. Then, we show that the physical sector is defined by three first-class constraints which preserve the full eleven-dimensional symmetry. Applying the same concepts to the eleven dimensional superparticle, taken off-shell, we discover a hidden twelve dimensional superPoincare symmetry that governs the theory.

hep-th↗
arXiv2003

Superstar in Noncommutative Superspace via Covariant Quantization of the Superparticle

A covariant quantization method is developed for the off-shell superparticle in 10 dimensions. On-shell it is consistent with lightcone quantization, while off-shell it gives a noncommutative superspace that realizes non-linearly a hidden 11-dimensional super Poincare symmetry. The non-linear commutation rules are then used to construct the supersymmetric generalization of the covariant Moyal star product in noncommutative superspace. As one of the possible applications, we propose this new product as the star product in supersymmetric string field theory. Furthermore, the formalism introduces new techniques and concepts in noncommutative (super)geometry.

hep-th↗
arXiv2000

Properties of perturbative solutions of unilateral matrix equations

A left-unilateral matrix equation is an algebraic equation of the form $$ a_0+a_1 x+a_2 x^2+... +a_n x^n=0 $$ where the coefficients $a_r$ and the unknown $x$ are square matrices of the same order and all coefficients are on the left (similarly for a right-unilateral equation). Recently certain perturbative solutions of unilateral equations and their properties have been discussed. We present a unified approach based on the generalized Bezout theorem for matrix polynomials. Two equations discussed in the literature, their perturbative solutions and the relation between them are described. More abstractly, the coefficients and the unknown can be taken as elements of an associative, but possibly noncommutative, algebra.

hep-th↗
arXiv2000

Proof of a Symmetrized Trace Conjecture for the Abelian Born-Infeld Lagrangian

In this paper we prove a conjecture regarding the form of the Born-Infeld Lagrangian with a U(1)^2n gauge group after the elimination of the auxiliary fields. We show that the Lagrangian can be written as a symmetrized trace of Lorentz invariant bilinears in the field strength. More generally we prove a theorem regarding certain solutions of unilateral matrix equations of arbitrary order. For solutions which have perturbative expansions in the matrix coefficients, the solution and all its positive powers are sums of terms which are symmetrized in all the matrix coefficients and of terms which are commutators.

hep-th↗
arXiv2000

Nonlinear Self-Duality in Even Dimensions

We show that the Born-Infeld theory with n complex abelian gauge fields written in an auxiliary field formulation has a U(n,n) duality group. We conjecture the form of the Lagrangian obtained by eliminating the auxiliary fields and then introduce a new reality structure leading to a Born-Infeld theory with n real fields and an Sp(2n,R) duality symmetry. The real and complex constructions are extended to arbitrary even dimensions. The maximal noncompact duality group is U(n,n) for complex fields. For real fields the duality group is Sp(2n,R) if half of the dimension of space-time is even and O(n,n) if it is odd. We also discuss duality under the maximal compact subgroup, which is the self-duality group of the theory obtained by fixing the expectation value of a scalar field. Supersymmetric versions of self-dual theories in four dimensions are also discussed.

hep-th↗
arXiv1999

Duality Invariant Born-Infeld Theory

We present an Sp(2n,R) duality invariant Born-Infeld U(1)^2n gauge theory with scalar fields. To implement this duality we had to introduce complex gauge fields and as a result the rank of the duality group is only half as large as that of the corresponding Maxwell gauge theory with the same number of gauge fields. The latter is self-dual under Sp(4n,R), the largest allowed duality group. A special case appears for n=1 when one can also write an SL(2,R) duality invariant Born-Infeld theory with a real gauge field. We also describe the supersymmetric version of the above construction.

hep-th↗
arXiv1999

Dualities of the Matrix Model from T-Duality of the Type II String

We investigate in the Matrix theory framework, the subgroup of dualities of the DLCQ of M-theory compactified on three-tori, which corresponds to T-duality in the auxiliary Type II string theory. We show how these dualities are realized in the supersymmetric Yang-Mills gauge theories on dual noncommutative three-tori.

hep-th↗