arXiv subjects

Fiorenzo Bastianelli

Publications and source records attributed to Fiorenzo Bastianelli.

At least 55 records · Page 3Linked to original sources

arXiv2008

Gravitational corrections to the Euler-Heisenberg Lagrangian

We use the worldline formalism for calculating the one-loop effective action for the Einstein-Maxwell background induced by charged scalars or spinors, in the limit of low energy and weak gravitational field but treating the electromagnetic field nonperturbatively. The effective action is obtained in a form which generalizes the standard proper-time representation of the Euler-Heisenberg Lagrangian. We compare with previous work and discuss possible applications.

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arXiv2008

The effective action in Einstein-Maxwell theory

Considerable work has been done on the one-loop effective action in combined electromagnetic and gravitational fields, particularly as a tool for determining the properties of light propagation in curved space. After a short review of previous work, I present some recent results obtained using the worldline formalism. In particular, I will discuss various ways of generalizing the QED Euler-Heisenberg Lagrangian to the Einstein-Maxwell case.

gr-qc↗

arXiv2008

Scalar heat kernel with boundary in the worldline formalism

The worldline formalism has in recent years emerged as a powerful tool for the computation of effective actions and heat kernels. However, implementing nontrivial boundary conditions in this formalism has turned out to be a difficult problem. Recently, such a generalization was developed for the case of a scalar field on the half-space R_+ x R^{D-1}, based on an extension of the associated worldline path integral to the full R^D using image charges. We present here an improved version of this formalism which allows us to write down non-recursive master formulas for the n-point contribution to the heat kernel trace of a scalar field on the half-space with Dirichlet or Neumann boundary conditions. These master formulas are suitable to computerization. We demonstrate the efficiency of the formalism by a calculation of two new heat-kernel coefficients for the half-space, a_4 and a_{9/2}.

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arXiv2008

Spinning particles and higher spin fields on (A)dS backgrounds

Spinning particle models can be used to describe higher spin fields in first quantization. In this paper we discuss how spinning particles with gauged O(N) supersymmetries on the worldline can be consistently coupled to conformally flat spacetimes, both at the classical and at the quantum level. In particular, we consider canonical quantization on flat and on (A)dS backgrounds, and discuss in detail how the constraints due to the worldline gauge symmetries produce geometrical equations for higher spin fields, i.e. equations written in terms of generalized curvatures. On flat space the algebra of constraints is linear, and one can integrate part of the constraints by introducing gauge potentials. This way the equivalence of the geometrical formulation with the standard formulation in terms of gauge potentials is made manifest. On (A)dS backgrounds the algebra of constraints becomes quadratic, nevertheless one can use it to extend much of the previous analysis to this case. In particular, we derive general formulas for expressing the curvatures in terms of gauge potentials and discuss explicitly the cases of spin 2, 3 and 4.

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arXiv2007

Scalar Field with Robin Boundary Conditions in the Worldline Formalism

The worldline formalism has been widely used to compute physical quantities in quantum field theory. However, applications of this formalism to quantum fields in the presence of boundaries have been studied only recently. In this article we show how to compute in the worldline approach the heat kernel expansion for a scalar field with boundary conditions of Robin type. In order to describe how this mechanism works, we compute the contributions due to the boundary conditions to the coefficients A_1, A_{3/2} and A_2 of the heat kernel expansion of a scalar field on the positive real line.

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arXiv2007

Worldline approach to quantum field theories on flat manifolds with boundaries

We study a worldline approach to quantum field theories on flat manifolds with boundaries. We consider the concrete case of a scalar field propagating on R_+ x R^{D-1} which leads us to study the associated heat kernel through a one dimensional (worldline) path integral. To calculate the latter we map it onto an auxiliary path integral on the full R^D using an image charge. The main technical difficulty lies in the fact that a smooth potential on R_+ x R^{D-1} extends to a potential which generically fails to be smooth on R^D. This implies that standard perturbative methods fail and must be improved. We propose a method to deal with this situation. As a result we recover the known heat kernel coefficients on a flat manifold with geodesic boundary, and compute two additional ones, A_3 and A_{7/2}. The calculation becomes sensibly harder as the perturbative order increases, and we are able to identify the complete A_{7/2} with the help of a suitable toy model. Our findings show that the worldline approach is viable on manifolds with boundaries. Certainly, it would be desirable to improve our method of implementing the worldline approach to further simplify the perturbative calculations that arise in the presence of non-smooth potentials.

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arXiv2007

Higher spin fields from a worldline perspective

Higher spin fields in four dimensions, and more generally conformal fields in arbitrary dimensions, can be described by spinning particle models with a gauged SO(N) extended supergravity on the worldline. We consider here the one-loop quantization of these models by studying the corresponding partition function on the one-dimensional torus. After gauge fixing the supergravity multiplet, the partition function reduces to an integral over the corresponding moduli space which is computed using orthogonal polynomial techniques. We obtain a compact formula which gives the number of physical degrees of freedom for all N in all dimensions. As an aside we compute the physical degrees of freedom of the SO(4) = SU(2)xSU(2) model with only a SU(2) factor gauged, which has attracted some interest in the literature.

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arXiv2005

Worldline approach to vector and antisymmetric tensor fields II

We extend the worldline description of vector and antisymmetric tensor fields coupled to gravity to the massive case. In particular, we derive a worldline path integral representation for the one-loop effective action of a massive antisymmetric tensor field of rank p (a massive p-form) whose dynamics is dictated by a standard Proca-like lagrangian coupled to a background metric. This effective action can be computed in a proper time expansion to obtain the corresponding Seeley-DeWitt coefficients a0, a1, a2. The worldline approach immediately shows that these coefficients are derived from the massless ones by the simple shift D -> D+1, where D is the spacetime dimension. Also, the worldline representation makes it simple to derive exact duality relations. Finally, we use such a representation to calculate the one-loop contribution to the graviton self-energy due to both massless and massive antisymmetric tensor fields of arbitrary rank, generalizing results already known for the massless spin 1 field (the photon).

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arXiv2005

Path integrals in curved space and the worldline formalism

We describe how to construct and compute unambiguously path integrals for particles moving in a curved space, and how these path integrals can be used to calculate Feynman graphs and effective actions for various quantum field theories with external gravity in the framework of the worldline formalism. In particular, we review a recent application of this worldline approach and discuss vector and antisymmetric tensor fields coupled to gravity. This requires the construction of a path integral for the N=2 spinning particle, which is used to compute the first three Seeley-DeWitt coefficients for all p-form gauge fields in all dimensions and to derive exact duality relations.

hep-th↗

arXiv2005

Worldline approach to vector and antisymmetric tensor fields

The N=2 spinning particle action describes the propagation of antisymmetric tensor fields, including vector fields as a special case. In this paper we study the path integral quantization on a one-dimensional torus of the N=2 spinning particle coupled to spacetime gravity. The action has a local N=2 worldline supersymmetry with a gauged U(1) symmetry that includes a Chern-Simons coupling. Its quantization on the torus produces the one-loop effective action for a single antisymmetric tensor. We use this worldline representation to calculate the first few Seeley-DeWitt coefficients for antisymmetric tensor fields of arbitrary rank in arbitrary dimensions. As side results we obtain the correct trace anomaly of a spin 1 particle in four dimensions as well as exact duality relations between differential form gauge fields. This approach yields a drastic simplification over standard heat-kernel methods. It contains on top of the usual proper time a new modular parameter implementing the reduction to a single tensor field. Worldline methods are generically simpler and more efficient in perturbative computations then standard QFT Feynman rules. This is particularly evident when the coupling to gravity is considered.

hep-th↗

arXiv2005

Dimensional regularization for N=1 susy sigma models and the worldline formalism

We generalize the worldline formalism to include spin 1/2 fields coupled to gravity. To this purpose we first extend dimensional regularization to supersymmetric nonlinear sigma models in one dimension. We consider a finite propagation time and find that dimensional regularization is a manifestly supersymmetric regularization scheme, since the classically supersymmetric action does not need any counterterm to preserve worldline supersymmetry. We apply this regularization scheme to the worldline description of Dirac fermions coupled to gravity. We first compute the trace anomaly of a Dirac fermion in 4 dimensions, providing an additional check on the regularization with finite propagation time. Then we come to the main topic and consider the one-loop effective action for a Dirac field in a gravitational background. We describe how to represent this effective action as a worldline path integral and compute explicitly the one- and two-point correlation functions, i.e. the spin 1/2 particle contribution to the graviton tadpole and graviton self-energy. These results are presented for the general case of a massive fermion. It is interesting to note that in the worldline formalism the coupling to gravity can be described entirely in terms of the metric, avoiding the introduction of a vielbein. Consequently, the fermion--graviton vertices are always linear in the graviton, just like the standard coupling of fermions to gauge fields.

hep-th↗

arXiv2005

One loop photon-graviton mixing in an electromagnetic field: Part 1

Photon-graviton mixing in an electromagnetic field is a process of potential interest for cosmology and astrophysics. At the tree level it has been studied by many authors. We consider the one-loop contribution to this amplitude involving a charged spin 0 or spin 1/2 particle in the loop and an arbitrary constant field. In the first part of this article, the worldline formalism is used to obtain a compact two-parameter integral representation for this amplitude, valid for arbitrary photon energies and background field strengths. The calculation is manifestly covariant througout.

gr-qc↗

arXiv2004

BRST treatment of zero modes for the worldline formalism in curved space

One-loop quantities in QFT can be computed in an efficient way using the worldline formalism. The latter rests on the ability of calculating 1D path integrals on the circle. In this paper we give a systematic discussion for treating zero modes on the circle of 1D path integrals for both bosonic and supersymmetric nonlinear sigma models, following an approach originally introduced by Friedan. We use BRST techniques and place a special emphasis on the issue of reparametrization invariance. Various examples are extensively analyzed to verify and test the general set-up. In particular, we explicitly check that the chiral anomaly, which can be obtained by the semiclassical approximation of a supersymmetric 1D path integral, does not receive higher order worldline contributions, as implied by supersymmetry.

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arXiv2002

Worldline formalism in a gravitational background

We analyze the worldline formalism in the presence of a gravitational background. In the worldline formalism a path integral is used to quantize the worldline coordinates of the particles. Contrary to the simpler cases of scalar and vector backgrounds, external gravity requires a precise definition of the ultraviolet regularization of the path integral. Taking into account the UV regularization, we describe the first quantized representation of the one-loop effective action for a scalar particle. We compute explicitly the contribution to the graviton tadpole and self-energy to test the validity of the method. The results obtained by usual field theoretical Feynman diagrams are reproduced in an efficient way. Finally, we comment on the technical problems related to the factorization of the zero mode from the path integral on the circle.

hep-th↗

arXiv2001

Simplified Method for Trace Anomaly Calculations in d=6 and d<6

We discuss a simplified method for computing trace anomalies in d=6 and d<6 dimensions. It is known that in the quantum mechanical approach trace anomalies in d dimensions are given by a (1+d/2)-loop computation in an auxiliary 1d sigma model with arbitrary geometry. We show how one can obtain the same information using a simpler d/2-loop calculation on an arbitrary geometry supplemented by a (1+d/2)-loop calculation on the simplified geometry of a maximally symmetric space.

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arXiv2000

6D trace anomalies from quantum mechanical path integrals

We use the recently developed dimensional regularization (DR) scheme for quantum mechanical path integrals in curved space and with a finite time interval to compute the trace anomalies for a scalar field in six dimensions. This application provides a further test of the DR method applied to quantum mechanics. It shows the efficiency in higher loop computations of having to deal with covariant counterterms only, as required by the DR scheme.

hep-th↗

arXiv2000

3-point functions of universal scalars in maximal SCFTs at large N

We compute all 3-point functions of the ``universal'' scalar operators contained in the interacting, maximally supersymmetric CFTs at large N by using the AdS/CFT correspondence. These SCFTs are related to the low energy description of M5, M2 and D3 branes, and the common set of universal scalars corresponds through the AdS/CFT relation to the fluctuations of the metric and the magnetic potential along the internal manifold. For the interacting (0,2) SCFT_6 at large N, which is related to M5 branes, this set of scalars is complete, while additional non-universal scalar operators are present in the d=4, N=4 super Yang-Mills theory and in the N=8 SCFT_3, related to D3 and M2 branes, respectively.

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arXiv1999

Three Point Functions for a Class of Chiral Operators in Maximally Supersymmetric CFT at Large N

We present a calculation of three point functions for a class of chiral operators, including the primary ones, in d = 3, N = 8; d = 6, N = (2,0) and d = 4, N = 4 superconformal field theories at large N. These theories are related to the infrared world-volume descriptions of N coincident M2, M5 and D3 branes, respectively. The calculation is done in the framework of the AdS/CFT correspondence and can be given a unified treatment employing a gravitational action in arbitrary dimensions D, coupled to a p+1 form and suitably compactified on AdS(D-2-p) x S(2+p). The interesting cases are obtained setting (D,p) to the values (11,5), (11,2) and (10,3).

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