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Kurt Lechner

Publications and source records attributed to Kurt Lechner.

34 records · Page 2Linked to original sources
arXiv2004

Intersecting D-branes, Chern-kernels and the inflow mechanism

We analyse a system of arbitrarily intersecting D-branes in ten-dimensional supergravity. Chiral anomalies are supported on the intersection branes, called I-branes. For non-transversal intersections anomaly cancellation has been realized until now only cohomologically but not locally, due to short-distance singularities. In this paper we present a consistent local cancellation mechanism, writing the delta-like brane currents as differentials of the recently introduced Chern--kernels, J=dK. In particular, for the first time we achieve anomaly cancellation for dual pairs of D-branes. The Chern-kernel approach allows to construct an effective action for the RR-fields which is free from singularities and cancels the quantum anomalies on all D-branes and I-branes.

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arXiv2004

Intersecting M2- and M5-branes

If an M2-brane intersects an M5-brane the canonical Wess-Zumino action is plagued by a Dirac-anomaly, i.e. a non-integer change of the action under a change of Dirac-brane. We show that this anomaly can be eliminated at the expense of a gravitational anomaly supported on the intersection manifold. Eventually we check that the last one is cancelled by the anomaly produced by the fermions present. This provides a quantum consistency check of these intersecting configurations.

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arXiv2003

Chern-kernels and anomaly cancellation in M-theory

This paper deals with magnetic equations of the type dH=J where the current J is a delta-function on a brane worldvolume and H a p-form field strength. In many situations in M-theory this equation needs to be solved for H in terms of a potential. A standard universality class of solutions, involving Dirac-branes, gives rise to strong intermediate singularities in H which in many physically relevant cases lead to inconsistencies. In this paper we present an alternative universality class of solutions for magnetic equations in terms of Chern-kernels, and provide relevant applications, among which the anomaly-free effective action for open M2-branes ending on M5-branes. The unobservability of the Dirac-brane requires a Dirac quantization condition; we show that the requirement of ``unobservability'' of the Chern-kernel leads in M-theory to classical gravitational anomalies which cancel precisely their quantum counterparts.

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arXiv2002

NS5-branes in IIA supergravity and gravitational anomalies

We construct a gravitational-anomaly-free effective action for the coupled system of IIA D=10 dynamical supergravity interacting with an NS5-brane. The NS5-brane is considered as elementary in that the associated current is a delta-function supported on its worldvolume. Our approach is based on a Chern-kernel which encodes the singularities of the three-form field strength near the brane in an SO(4)-invariant way and provides a solution for its Bianchi identity in terms of a two-form potential. A dimensional reduction of the recently constructed anomaly-free effective action for an elementary M5-brane in D=11 is seen to reproduce our ten-dimensional action. The Chern-kernel approach provides in particular a concrete realization of the anomaly cancellation mechanism envisaged by Witten.

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arXiv2001

Dirac Branes, Characteristic Currents and Anomaly Cancellations in 5-Branes

The aim of this note is to discuss, in a somewhat informal language, the cancellation of anomalies (in topologically trivial space-time) for 5-branes using as "building blocks": i) a generalization to p-branes of the Dirac strings of monopoles (Dirac branes) and a refinement of this idea involving a geometric regularization of Dirac branes, leading to the formalism of "characteristic currents" ii) the PST formalism . As an example of the potentiality of the developed framework we discuss in some detail the anomaly cancellation in the D=10 effective theory of heterotic string and 5-brane coupled to supergravity, where the anomaly inflow is automatically generated. Some remarks are also made on a similar approach to the problem of anomaly cancellation in the effective theory of M5-brane coupled to D=11 supergravity, developed in collaboration with M.Tonin, where however still as open problem remains a Dirac anomaly.

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arXiv2000

A Quantum field theory of dyons

We construct a classical field theory action which upon quantization via the functional integral approach, gives rise to a consistent Dirac-string independent quantum field theory. The approach entails a systematic derivation of the correlators of all gauge invariant observables, and also of charged dyonic fields. Manifest SO(2)-duality invariance and Lorentz invariance are ensured by the PST-approach.

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arXiv1998

D=10, N=IIB Supergravity: Lorentz-invariant actions and duality

We present a manifestly Lorentz invariant and supersymmetric component field action for $D = 10$, type $IIB$ supergravity, using a newly developed method for the construction of actions with chiral bosons, which implies only a single scalar non propagating auxiliary field. With the same method we construct also an action in which the complex two-form gauge potential and its Hodge-dual, a complex six-form gauge potential, appear in a symmetric way in compatibility with supersymmetry and Lorentz invariance. The duals of the two physical scalars of the theory turn out to be described by a $SL(2,R)$ triplet of eight-forms whose curvatures are constrained by a single linear relation. We present also a supersymmetric action in which the basic fields and their duals, six-form and eight-form potentials, appear in a symmetric way. All these actions are manifestly invariant under the global $SL(2,R)$-duality group of $D = 10$, $IIB$ supergravity and are equivalent to each other in that their dynamics corresponds to the well known equations of motion of $ D=10$, $IIB$ supergravity.

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arXiv1998

Self-dual tensors and gravitational anomalies in 4n+2 dimensions

Starting from a manifestly Lorentz- and diffeomorphism-invariant classical action we perform a perturbative derivation of the gravitational anomalies for chiral bosons in 4n+2 dimensions. The manifest classical invariance is achieved using a newly developed method based on a scalar auxiliary field and two new bosonic local symmetries. The resulting anomalies coincide with the ones predicted by the index theorem. In the two-dimensional case, moreover, we perform an exact covariant computation of the effective action for a chiral boson (a scalar) which is seen to coincide with the effective action for a two-dimensional complex Weyl-fermion. All these results support the quantum reliability of the new, at the classical level manifestly invariant, method.

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arXiv1997

Covariant actions for chiral supersymmetric bosons

We review a recently developed covariant Lagrangian formulation for $p$--forms with (anti)self-dual field-strengths and present its extension to the supersymmetric case. As explicit examples we construct covariant Lagrangians for six-dimensional models with N=1 rigid and curved supersymmetry.

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arXiv1997

N = 1, D = 6 Supergravity: Duality and non Minimal Couplings

In this paper we present a superspace formulation of $N = 1, D = 6$ supergravity with one tensor-multiplet and an arbitrary number of vector- and hypermultiplets, in which the bosonic abelian superforms of the theory, the dilaton, the abelian gauge fields and the two-form are replaced by their S-duals i.e. four, three and two-superforms respectively, in compatibility with supersymmetry. As usual this replacement interchanges Bianchi identities with equations of motion. This formulation holds in the presence of one tensor multiplet and arbitrary numbers of hypermultiplets and abelian super-Maxwell multiplets if all couplings are minimal. We determine the consistency conditions for non-minimal couplings in $N = 1$, $D = 6$ supergravity, for which we present a particularly significant solution, namely the one associated with the Chern-Simons-Lorentz three-form which entails the Green-Schwarz anomaly cancellation mechanism. In the case of non minimal couplings it is found that the gauge fields and the two-form can still be dualized while the dilaton has to remain a zero-form.

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arXiv1997

On the equivalence of different formulations of the M Theory five--brane

We show that the field equations for the supercoordinates and the self--dual antisymmetric tensor field derived from the recently constructed kappa-invariant action for the M theory five-brane are equivalent to the equations of motion obtained in the doubly supersymmetric geometrical approach at the worldvolume component level.

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arXiv1996

World-manifold and target space anomalies in heterotic Green-Schwarz strings and five-branes

The quantum consistency of sigma-models describing the dynamics of extended objects in a curved background requires the cancellation of their world-volume anomalies, which are conformal anomalies for the heterotic string and $SO(1,5)$ Lorentz-anomalies for the heterotic five-brane, and of their ten dimensional target space anomalies. In determining these anomalies in a $D=10$ Lorentz-covariant back-ground gauge we find that for the heterotic string the worldvolume anomalies cancel for 32 heterotic fermions while for the conjectured heterotic five-brane they cancel for only 16 heterotic fermions, this result being in contrast with the string/five-brane duality conjecture. For what concerns the target space anomalies we find that the five-brane eight-form Lorentz-anomaly polynomial differs by a factor of $1/2$ from what is expected on the basis of duality. Possible implications of these results are discussed.

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arXiv1995

Seven--Superform Gauge Fields in N=1, D=10 Supergravity and Duality

We present a formulation of $N=1,D=10$ Supergravity--Super--Maxwell theory in superspace in which the graviphoton can be described by a 2--form $B_2$ or a 6--form $B_6$, the photon by a 1--form $A_1$ or a 7--form $A_7$ and the dilaton by a scalar $φ$ or an 8--form $φ_8$, the supercurvatures of these fields being related by duality. Duality interchanges Bianchi identities and equations of motion for each of the three couples of fields. This construction envisages the reformulation of $D=10$ Supergravity, involving 7--forms as gauge fields, conjectured by Schwarz and Sen, which, upon toroidal compactification to four dimensions, gives the manifestly $SL(2,R)_S$ invariant form of the heterotic string effective action.

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arXiv1995

String k-anomalies and D=10 Supergravity constraints: the solution of a puzzle

The $κ$--anomaly cancellation mechanism in the heterotic superstring determines the superspace constraints for N=1, D=10 Supergravity--Super--Yang--Mills theory. We point out that the constraints found recently in this way appear to disagree with superspace solutions found in the past. We solve this puzzle establishing perfect agreement between the two methods.

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