non-Abelian Born-Infeld Theory Research Articles

On unified field theories, dynamical torsion and geometrical models: II

A new model of a nondualistic unified theory is proposed. This model is absolutely consistent from the mathematical and geometrical points of view and is based on a manifold equipped with an underlying hypercomplex structure and zero nonmetricity. Also we showed that interesting wormhole solutions, similar to the non-Abelian Born-Infeld theory of our previous work [14] can be obtained. The solution of this model is explicitly compared with our previous one and we find that the torsion plays in this unified theory a role similar to that of Yang-Mills type strength field coming from the non-Abelian Born-Infeld energy momentum tensor. The meaning of the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time) is completely elucidated.

Interacting D2 branes in ten dimensions and non-Abelian Born–Infeld theory

In this paper we extend the bosonic D-brane action in D = 10 obtained by duality from the D = 11 membrane wrapped on S1 to an SU(2) non-Abelian system. This system presents only first class constraints, whose algebra closes off-shell and generalizes the algebra of diffeomorphisms of the D2 brane to include non-Abelian symmetry generators. From the SU(2)D-brane action, we also obtain the SU(2) Born–Infeld theory by performing a covariant reduction to a flat background. This calculation agrees up to fourth order with the result obtained from the superstring amplitudes and gives an alternative approach to analyse non-Abelian Born–Infeld theories.

NON-ABELIAN BORN–INFELD THEORY WITHOUT THE SQUARE-ROOT

A non-Abelian Born–Infeld theory is presented. Its construction does not require the square-root structure that characterizes the Dirac–Born–Infeld (DBI) action. The procedure is based on an Abelian theory proposed by Schrödinger that, as he showed, is equivalent to Born–Infeld theory. Various non-Abelian generalizations are possible. We focus our attention on one of them. For it, it is shown that instantons solutions exist. Our formalism could be of interest in connection with string theory and possible extensions of well-known physical results in the usual Born–Infeld Abelian case.

Generalizations of Yang–Mills theory with nonlinear constitutive equations

We generalize classical Yang-Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain conditions on the constitutive equations specifying the Lagrangian case, of which recently-discussed non-Abelian Born-Infeld theories are particular examples. Some models in our class possess nontrivial Galilean (c goes to infinity) limits; we determine when such limits exist, and obtain them explicitly.

The open superstring and the non-abelian born-infeld theory

Abstract In the recent years new interest has arised in determining the Superstring Theory corrections to the Yang-Mills lagrangian. For a long time only the O (α′ 2 ) terms were known, together with some partial knowledge of the O (α′ 3 ) ones. On this contribution we report in the recent progress on this subject, carried over in the last two years, emphasizing the scattering amplitude approach and the recent calculation of the five-point amplitude.

Abelian and nonabelian vector field effective actions from string field theory

The leading terms in the tree-level effective action for the massless fields of the bosonic open string are calculated by integrating out all massive fields in Witten's cubic string field theory. In both the abelian and nonabelian theories, field redefinitions make it possible to express the effective action in terms of the conventional field strength. The resulting actions reproduce the leading terms in the abelian and nonabelian Born-Infeld theories, and include (covariant) derivative corrections.

Stabilization of Yang-Mills chaos in non-Abelian Born-Infeld theory

We investigate dynamics of the homogeneous time-dependent SU(2) Yang-Mills fields governed by the non-Abelian Born-Infeld lagrangian which arises in superstring theory as a result of summation of all orders in the string slope parameter $\alpha'$. It is shown that generically the Born-Infeld dynamics is less chaotic than that in the ordinary Yang-Mills theory, and at high enough field strength the Yang-Mills chaos is stabilized. More generally, a smothering effect of the string non-locality on behavior of classical fields is conjectured.

FRW wormhole instantons in the non-Abelian Born-Infeld theory

A family of wormhole instanton solutions is obtained in the non-Abelian Born-Infeld theory in the presence of a positive cosmological constant. These wormholes have a closed Friedmann-Robertson-Walker geometry and a nontrivial SO(4)-symmetric gauge sector. It is found that when the matter sector in the action is dominated by Born-Infeld terms inducing a string gas behavior, then no wormhole solutions are admissible. However, when the gauge fields asymptotically lead to a radiation scenario, wormhole solutions become possible. The presence of Born-Infeld perturbations in this stage determines specific modifications for the wormhole dynamics. Some of these physical implications are consequently discussed. In particular, we comment on how they can modify the quantization in energy levels of the wormhole solution. We also mention how this may affect the quantization of topological charges and conservation of fermion number.

Dyons in non-Abelian Born-Infeld theory

We analyze a nonabelian extension of Born--Infeld action for the SU(2) group. In the class of spherically symmetric solutions we find that, besides the Gal'tsov--Kerner glueballs, only the analytic dyons have finite energy. The presented analytic and numerical investigation excludes the existence of pure magnetic monopoles of 't Hooft--Polyakov type.

D-brane effective field theory from string field theory

Open string field theory is considered as a tool for deriving the effective action for the massless or tachyonic fields living on D-branes. Some simple calculations are performed in open bosonic string field theory which validate this approach. The level truncation method is used to calculate successive approximations to the quartic terms \phi^4, (A^\mu A_\mu)^2 and [A_\mu, A_\nu]^2 for the zero momentum tachyon and gauge field on one or many bosonic D-branes. We find that the level truncation method converges for these terms within 2-4% when all massive fields up to level 20 are integrated out, although the convergence is slower than exponential. We discuss the possibility of extending this work to determine the structure of the nonabelian Born-Infeld theory describing the gauge field on a system of many parallel bosonic or supersymmetric D-branes. We also describe a brane configuration in which tachyon condensation arises in both the gauge theory and string field theory pictures. This provides a natural connection between recent work of Sen and Zwiebach on tachyon condensation in string field theory and unstable vacua in super Yang-Mills and Born-Infeld field theory.

Noncommutative/nonlinear BPS equations without zero slope limit

It is widely believed that via the Seiberg-Witten map, the linearly realized BPS equation in the non-commutative space is related to the non-linearly realized BPS equation in the commutative space in the zero slope limit. We show that the relation also holds without taking the zero slope limit as is expected from the arguments of the BPS equation for the non-Abelian Born-Infeld theory. This is regarded as an evidence for the relation between the two BPS equations. As a byproduct of our analysis, the non-linear instanton equation is solved exactly.

Non-abelian Born–Infeld versus string theory

Motivated by the results of Hashimoto and Taylor, we perform a detailed study of the mass spectrum of the non-abelian Born-Infeld theory, defined by the symmetrized trace prescription, on tori with constant magnetic fields turned on. Subsequently, we compare this for several cases to the mass spectrum of intersecting D-branes. Exact agreement is found in only two cases: BPS configurations on the four-torus and coinciding tilted branes. Finally we investigate the fluctuation dynamics of an arbitrarily wrapped Dp-brane with flux.

Classical glueballs in non-Abelian Born-Infeld theory.

It is shown that the Born-Infeld-type modification of the quadratic Yang-Mills action gives rise to classical particlelike solutions prohibited in the standard Yang-Mills theory. This becomes possible due to breaking of the scale invariance by the Born-Infeld nonlinearity. New classical glueballs, which are of a sphaleronic nature, exhibit a striking similarity to the Bartnik-McKinnon solutions to the Yang-Mills theory coupled to gravity.

BPS states of the non-abelian Born–Infeld action

We argue that the trace structure of the non-abelian Born–Infeld action can be fixed by demanding that the action be linearised by certain energy-minimising BPS-like configurations. It is shown how instantons in D4-branes, SU(2) monopoles and dyons in D3-branes, and vortices in D2-branes are all BPS states of the action recently proposed by Tseytlin. All such configurations can be dealt with exactly within the context of non-abelian Born–Infeld theory since, given the relevant BPS-like condition, the action reduces to that of Yang–Mills theory. It would seem, moreover, that such an analysis holds for the symmetrised trace structure of Tseytlin's proposal only.