Supersymmetric Born-Infeld Action Research Articles

Supersymmetric Born-Infeld actions and new Fayet-Iliopoulos terms

We consider mathcal{N} = 1 supersymmetric Born-Infeld actions that have a second non-linear supersymmetry. We focus on the model proposed by Bagger and Galperin and show that the breaking of the second supersymmetry is sourced by the new Fayet-Iliopoulos D-term. Interpreting such an action as the effective theory of a space-filling (anti) D3-brane leads to an expression for the new Fayet-Iliopoulos parameter in terms of the brane tension and α′.

D2-brane within coset approach

In this notes, we derive the component on-shell action of the space-filling D2-brane, i.e. N = 1, d = 3 supersymmetric Born-Infeld action within the nonlinear realization approach. The Bianchi identity admits direct covariantization with respect to the broken N = 1, d = 3 supersymmetry. In the corresponding on-shell component action all fermionic terms combine into covariant, with respect to broken supersymmetry, objects: covariant derivatives and fierbein and therefore the D2-brane component action has very simple form. Similarly to the cases of p-branes, it mimics the bosonic Born-Infeld action.

Nilpotent chiral superfield in N = 2 $$ \mathcal{N}=2 $$ supergravity and partial rigid supersymmetry breaking

In the framework of N=2 conformal supergravity in four dimensions, we introduce a nilpotent chiral superfield suitable for the description of partial supersymmetry breaking in maximally supersymmetric spacetimes. As an application, we construct Maxwell-Goldstone multiplet actions for partial N=2 --> N=1 supersymmetry breaking on R x S^3, AdS_3 x S^1 (or its covering AdS_3 x R), and a pp-wave spacetime. In each of these cases, the action coincides with a unique curved-superspace extension of the N=1 supersymmetric Born-Infeld action, which is singled out by the requirement of U(1) duality invariance.

Space-filling D3-brane within coset approach

We derive the component on-shell action of the space-filling D3-brane, {\it i.e.} $N=1$ supersymmetric Born-Infeld action, within the nonlinear realization approach. The covariant Bianchi identity defining the $N=1$, $d=4$ vector supermultiplet has been constructed by introducing a new bosonic Goldstone superfield associated with the generator of the $U(1)$ group, which transforms to each other the spinor generators of unbroken and spontaneously broken $N=1$, $d=4$ supersymmetries. The first component of this Goldstone superfield is the auxiliary field of the vector supermultiplet and, therefore, the Bianchi identity can be properly defined. The component action of the D3-brane has a very simple form, being written in terms of derivatives covariant with respect to spontaneously broken supersymmetry - it just mimics its bosonic counterpart.

Massive Born-Infeld and other dual pairs

We consider massive dual pairs of p-forms and (D-p-1)-forms described by non-linear Lagrangians, where non-linear curvature terms in one theory translate into non-linear mass-like terms in the dual theory. In particular, for D=2p and p even the two non-linear structures coincide when the non-linear massless theory is self-dual. This state of affairs finds a natural realization in the four-dimensional massive N=1 supersymmetric Born-Infeld action, which describes either a massive vector multiplet or a massive linear (tensor) multiplet with a Born-Infeld mass-like term. These systems should play a role for the massive gravitino multiplet obtained from a partial super-Higgs in N=2 Supergravity.

On the road to [formula omitted] supersymmetric Born–Infeld action

We analyze the exact perturbative solution of N=2 Born–Infeld theory which is believed to be defined by Ketovʼs equation. This equation can be considered as a truncation of an infinite system of coupled differential equations defining Born–Infeld action with one manifest N=2 and one hidden N=2 supersymmetries. We explicitly demonstrate that infinitely many new structures appear in the higher orders of the perturbative solution to Ketovʼs equation. Thus, the full solution cannot be represented as a function depending on a finite number of its arguments. We propose a mechanism for generating the new structures in the solution and show how it works up to 18-th order. Finally, we discuss two new superfield actions containing an infinite number of terms and sharing some common features with N=2 supersymmetric Born–Infeld action.

Fayet-Iliopoulos term and nonlinear self-duality

The N = 1 supersymmetric Born-Infeld action is known to describe the vector Goldstone multiplet for partially broken N = 2 rigid supersymmetry, and this model is believed to be unique. However, it can be deformed by adding the Fayet-Iliopoulos term without losing the second nonlinearly realized supersymmetry. Although the first supersymmetry then becomes spontaneously broken, the deformed action still describes partial N = 2 to N = 1 supersymmetry breaking. The unbroken supercharges in this theory correspond to a different choice of N = 1 subspace in the N = 2 superspace, as compared with the undeformed case. Implications of the Fayet-Iliopoulos term for general models for self-dual nonlinear supersymmetric electrodynamics are discussed. The known ubiquitous appearance of the Volkov-Akulov action in such models is explained. We also present a two-parameter duality-covariant deformation of the N = 1 supersymmetric Born-Infeld action as a model for partial breaking of N = 2 supersymmetry.

On the component structure of Script N = 1 supersymmetric nonlinear electrodynamics

We analyze the component structure of models for 4D N = 1 supersymmetric nonlinear electrodynamics that enjoy invariance under continuous duality rotations. The N = 1 supersymmetric Born-Infeld action is a member of this family. Such dynamical systems have a more complicated structure, especially in the presence of supergravity, as compared with well-studied effective supersymmetric theories containing at most two derivatives (including nonlinear Kahler sigma-models). As a result, when deriving their canonically normalized component actions, it becomes impractical and cumbersome to follow the traditional approach of (i) reducing to components; and then (ii) applying a field-dependent Weyl and local chiral transformation. It proves to be more efficient to follow the Kugo-Uehara scheme which consists of (i) extending the superfield theory to a super-Weyl invariant system; and then (ii) applying a plain component reduction along with imposing a suitable super-Weyl gauge condition. Here we implement this scheme to derive the bosonic action of self-dual supersymmetric electrodynamics coupled to the dilaton-axion chiral multiplet and a Kahler sigma-model. In the fermionic sector, the action contains higher derivative terms. In the globally supersymmetric case, a nonlinear field redefinition is explicitly constructed which eliminates all the higher derivative terms and brings the fermionic action to a one-parameter deformation of the Akulov-Volkov action for the Goldstino. The Akulov-Volkov action emerges, in particular, in the case of the N = 1 supersymmetric Born-Infeld action.

4D, N = 1 Born-Infeld supergravity

We propose the four-dimensional (4D), N = 1 supergravitational analogues (avatars) of the 4D, N = 1 supersymmetric Born-Infeld action in fourdimensions for the first time, by using superspace. In particular, a new Born-Infeld type generalization of the Weyl supergravity action is given. A natural new Born-Infeld type generalization of the Einstein supergravity is found as well. We also briefly discuss aconstruction of the 4D Born-Infeld-Einstein supergravityfrom the AdS supergravity in five dimensions, which seems to be verynatural in our approach.

DEFORMED SUPERSYMMETRIC FIELD THEORIES

We make a short review on the Moyal–Weyl star products with emphasis in its convergence. We consider field theories on a deformed superspace and analyze the compatibility of such products with supersymmetry. We investigate some aspects of the Wess–Zumino model, super-Yang–Mills theories and analyze the correspondence of the latter with the supersymmetric Born–Infeld action.

Actions and symmetries of NSR superstrings and D-strings

We present all NSR superstring and super-D-string actions invariant under a set of prescribed gauge transformations, and characterize completely their global symmetries. In particular we obtain locally supersymmetric Born–Infeld actions on general backgrounds in a formulation with extra target space dimensions. The nontrivial global symmetries of the superstring actions correspond to isometries of the background, whereas super-D-string actions can have additional symmetries acting nontrivially also on the coordinates of the extra dimensions.

Non-linear realization of ℵ -extended supersymmetry

As generalizations of the original Volkov-Akulov action in four-dimensions, actions are found for all space-time dimensions D invariant under N non-linear realized global supersymmetries. We also give other such actions invariant under the global non-linear supersymmetry. As an interesting consequence, we find a non-linear supersymmetric Born-Infeld action for a non-Abelian gauge group for arbitrary D and N, which coincides with the linearly supersymmetric Born-Infeld action in D=10 at the lowest order. For the gauge group U({\cal N}) for M(atrix)-theory, this model has {\cal N}^2-extended non-linear supersymmetries, so that its large {\cal N} limit corresponds to the infinitely many (\aleph_0) supersymmetries. We also perform a duality transformation from F_{\mu\nu} into its Hodge dual N_{\mu_1...\mu_{D-2}}. We next point out that any Chern-Simons action for any (super)groups has the non-linear supersymmetry as a hidden symmetry. Subsequently, we present a superspace formulation for the component results. We further find that as long as superspace supergravity is consistent, this generalized Volkov-Akulov action can further accommodate such curved superspace backgrounds with local supersymmetry, as a super p-brane action with fermionic kappa-symmetry. We further elaborate these results to what we call `simplified' (Supersymmetry)^2-models, with both linear and non-linear representations of supersymmetries in superspace at the same time. Our result gives a proof that there is no restriction on D or N for global non-linear supersymmetry. We also see that the non-linear realization of supersymmetry in `curved' space-time can be interpreted as `non-perturbative' effect starting with the `flat' space-time.

Multiple Dp-branes in weak background fields

We find the terms in the non-abelian world-volume action of a system of many Dp-branes which describe the leading coupling to all type II supergravity background fields. These results are found by T-dualizing earlier results for D0-branes, which in turn were determined from calculations of the M(atrix) theory description of the supercurrent of 11D supergravity. Our results are compatible with earlier results on the supersymmetric Born–Infeld action for a single D-brane in a general background and with Tseytlin's symmetrized trace proposal for extending the abelian Born–Infeld action to a non-abelian theory. In the case p=3, the operators we find on the D-brane world-volume are closely related to those which couple to supergravity fields in the AdS 5× S 5 IIB supergravity background. This gives an explicit construction, including normalization, of some of the operators used in the celebrated AdS/CFT correspondence for 3-branes. We also discuss the S-duality of the action in the case p=3, finding that the S-duality of the action determines how certain operators in the N=4 4D SYM theory transform under S-duality. These S-duality results give some new insight into the puzzle of the transverse 5-brane in M(atrix) theory.

( α′) 4 corrections to the N=2 supersymmetric Born–Infeld action

We consider the N=2 supersymmetric Born–Infeld action and compute one-loop divergences quantizing the theory in N=1 superspace. We find that in the presence of non constant curvature the theory is not renormalizable. The structure of the ( α′) 4 counterterm, proportional to derivatives of the curvature, is consistent with effective action calculations from superstring theory.

Born-Infeld-Goldstone superfield actions for gauge-fixed D5- and D3-branes in 6d

The supersymmetric Born-Infeld actions describing gauge-fixed D-5- and D3-branes in ambient six-dimensional (6d) space-time are constructed in superspace. A new 6d action is the (1,0) supersymmetric extension of the 6d Born-Infeld action. It is related via dimensional reduction to another remarkable 4d action describing the N = 2 supersymmetric extension of the Born-Infeld-Nambu-Goto action with two real scalats. Both actions are the Goldstone actions associated with partial ( 1 2 ) spontaneous breaking of extended supersymmetry having 16 supercharges down to 8 supercharges. Both actions can be put into the ‘non-linear sigma-model’ form by using certain non-linear superfield constraints. The unbroken supersymmetry is always linearly realised in our construction.

A MANIFESTLY N=2 SUPERSYMMETRIC BORN–INFELD ACTION

A manifestly N=2 supersymmetric completion of the four-dimensional Nambu–Goto–Born–Infeld action, which is self-dual with respect to electric–magnetic duality, is constructed in terms of an Abelian N=2 superfield strength W in the conventional N=2 superspace. A relation to the known N=1 supersymmetric Born–Infeld action in N=1 superspace is established. The action found can be considered either as the Goldstone action associated with a partial breaking of N=4 supersymmetry down to N=2, with the N=2 vector superfield being a Goldstone field, or, equivalently, as the gauge-fixed superfield action of a (D-3)-brane in flat six-dimensional ambient space–time.