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Jochen Zahn

Publications and source records attributed to Jochen Zahn.

At least 37 records · Page 2Linked to original sources
arXiv2019

Trace anomaly for chiral fermions via Hadamard subtraction

We calculate the trace (conformal) anomaly for chiral fermions in a general curved background using Hadamard subtraction. While in intermediate steps of the calculation imaginary terms proportional to the Pontryagin density appear, imposing a vanishing divergence of the stress tensor these terms completely cancel, and we recover the well-known result equal to half the trace anomaly of a Dirac fermion. We elaborate in detail on the advantages of the Hadamard method for the general definition of composite operators in general curved spacetimes, and speculate on possible causes for the appearance of the Pontryagin density in other calculations.

hep-th↗
arXiv2017

The semi-classical energy of the Chodos-Thorn string

We compute semi-classical corrections to the energy of rotating Nambu-Goto strings with masses at the ends, using methods from quantum field theory on curved space-times. In the limit of large angular momentum, we recover the Regge intercept $a = 1 + \frac{D-2}{24}$ for $D$ dimensional target space previously found for the open and closed string. [Result is wrong and corrected in 1605.07928]

hep-th↗
arXiv2017

Generalized Wentzell boundary conditions and quantum field theory

We discuss a free scalar field subject to generalized Wentzell boundary conditions. On the classical level, we prove well-posedness of the Cauchy problem and in particular causality. Upon quantization, we obtain a field that may naturally be restricted to the boundary. We discuss the holographic relation between this boundary field and the bulk field.

math-ph↗
arXiv2017

Classical phase space and Hadamard states in the BRST formalism for gauge field theories on curved spacetime

We investigate linearized gauge theories on globally hyperbolic spacetimes in the BRST formalism. A consistent definition of the classical phase space and of its Cauchy surface analogue is proposed. We prove that it is isomorphic to the phase space in the subsidiary condition approach of Hack and Schenkel in the case of Maxwell, Yang-Mills, and Rarita-Schwinger fields. Defining Hadamard states in the BRST formalism in a standard way, their existence in the Maxwell and Yang-Mills case is concluded from known results in the subsidiary condition (or Gupta-Bleuler) formalism. Within our framework, we also formulate criteria for non-degeneracy of the phase space in terms of BRST cohomology and discuss special cases. These include an example in the Yang-Mills case, where degeneracy is not related to a non-trivial topology of the Cauchy surface.

math-ph↗
arXiv2017

Global anomalies on Lorentzian space-times

We formulate an algebraic criterion for the presence of global anomalies on globally hyperbolic space-times in the framework of locally covariant field theory. We discuss some consequences and check that it reproduces the well-known global $SU(2)$ anomaly in four space-time dimensions.

hep-th↗
arXiv2015

The current density in quantum electrodynamics in time-dependent external potentials and the Schwinger effect

In the framework of quantum electrodynamics (QED) in external potentials, we introduce a method to compute the time-dependence of the expectation value of the current density for time-dependent homogeneous external electric fields. We apply it to the so-called Sauter pulse. For late times, our results agree with the asymptotic value due to electron-positron pair production. We correct, and compare to, a general expression derived by Serber for the linearization in the external field. Based on the properties of the current density, we argue that the appearance of enhanced quasi-particle densities at intermediate times in slowly varying sub-critical potentials is generic. Also an alternative approach, which circumvents these difficulties, is sketched.

hep-th↗
arXiv2015

The current density in quantum electrodynamics in external potentials

We review different definitions of the current density for quantized fermions in the presence of an external electromagnetic field. Several deficiencies in the popular prescription due to Schwinger and the mode sum formula for static external potentials are pointed out. We argue that Dirac's method, which is the analog of the Hadamard point-splitting employed in quantum field theory in curved space-times, is conceptually the most satisfactory. As a concrete example, we discuss vacuum polarization and the stress-energy tensor for massless fermions in 1+1 dimension. Also a general formula for the vacuum polarization in static external potentials in 3+1 dimensions is derived.

hep-th↗
arXiv2015

Self-intersecting fuzzy extra dimensions from squashed coadjoint orbits in ${\cal N}=4$ SYM and matrix models

We find new vacuum solutions of ${\cal N}=4$ super-Yang-Mills with totally anti-symmetric cubic soft SUSY breaking terms, or equivalently solutions of the IKKT matrix model of type $\mathbb{R}^4_θ\times {\cal K}_N$ with flux terms. The solutions can be understood in terms of 4- and 6- dimensional fuzzy branes ${\cal K}_N$ in extra dimensions, describing self-intersecting projections of compact flag manifolds of $SU(3)$. The 6-dimensional solutions provide a 6-fold covering of the internal space near the origin, while the 4-dimensional branes have a triple self-intersections spanning all 6 internal directions. The solutions have lower energy than the trivial vacuum, and we prove that there are no negative modes. The massless modes are identified explicitly. In particular there are chiral fermionic zero modes, linking the coincident sheets with opposite flux at the origin. They have a $\mathbb{Z}_3$ family symmetry, originating from the Weyl group rotations.

hep-th↗
arXiv2014

Locally covariant charged fields and background independence

We discuss gauge background independence at the example of the charged Dirac field. We show that a perturbative version of background independence, termed perturbative agreement by Hollands and Wald, can be fulfilled, and discuss some of its consequences.

math-ph↗
arXiv2014

An extended standard model and its Higgs geometry from the matrix model

We find a simple brane configuration in the IKKT matrix model which resembles the standard model at low energies, with a second Higgs doublet and right-handed neutrinos. The electroweak sector is realized geometrically in terms of two minimal fuzzy ellipsoids, which can be interpreted in terms of four point-branes in the extra dimensions. The electroweak Higgs connects these branes and is an indispensable part of the geometry. Fermionic would-be zero modes arise at the intersections with two larger branes, leading precisely to the correct chiral matter fields at low energy, along with right-handed neutrinos which can acquire a Majorana mass due to a Higgs singlet. The larger branes give rise to $SU(3)_c$, extended by $U(1)_B$ and another $U(1)$ which are anomalous at low energies and expected to disappear. At higher energies, mirror fermions and additional fields arise, completing the full ${\cal N}=4$ supersymmetry. The brane configuration is a solution of the model, assuming a suitable effective potential and a non-linear stabilization of the singlet Higgs. The basic results can be carried over to ${\cal N}=4$ $SU(N)$ super-Yang-Mills on ordinary Minkowski space with sufficiently large $N$.

hep-th↗
arXiv2014

Locally covariant chiral fermions and anomalies

We define chiral fermions in the presence of non-trivial gravitational and gauge background fields in the framework of locally covariant field theory. This allows to straightforwardly compute the chiral anomalies on non-compact Lorentzian space-times, without recourse to a weak field approximation.

hep-th↗
arXiv2013

The effective theory of strings

We show that the Nambu-Goto string, and its higher dimensional generalizations, can be quantized, in the sense of an effective theory, in any dimension of the target space. The crucial point is to consider expansions around classical string configurations. We are using tools from perturbative algebraic quantum field theory, quantum field theory on curved spacetimes, and the Batalin-Vilkovisky formalism. Our model has some similarities with the Lüscher-Weisz string, but we allow for arbitrary classical background string configurations and keep the diffeomorphism invariance.

math-ph↗
arXiv2013

An Index for Intersecting Branes in Matrix Models

We introduce an index indicating the occurrence of chiral fermions at the intersection of branes in matrix models. This allows to discuss the stability of chiral fermions under perturbations of the branes.

hep-th↗
arXiv2013

The renormalized locally covariant Dirac field

The definition of the locally covariant Dirac field is adapted such that it may be charged under a gauge group and in the presence of generic gauge and Yukawa background fields. We construct renormalized Wick powers and time-ordered products. It is shown that the Wick powers may be defined such that the current and the stress-energy tensor are conserved, and the remaining ambiguity is characterized. We sketch a variant of the background field method that can be used to determine the renormalization group flow at the one loop level from the nontrivial scaling of Wick powers.

math-ph↗
arXiv2013

Brane compactifications and 4-dimensional geometry in the IKKT model

We study in detail certain brane solutions with compact extra dimensions M^4 x K in the IKKT matrix model, with K being a two-dimensional rotating torus embedded in R^6. We focus on the compactification moduli and the fluctuations of K \subset R^6 and their physical significance. Mediated by the Poisson tensor, they contribute to the effective 4-dimensional metric on the brane, and thereby become gravitational degrees of freedom. We show that the zero modes corresponding to the global symmetries of the model lead to Ricci-flat 4-dimensional metric perturbations, wherever the energy-momentum tensor vanishes. Their coupling to the energy momentum tensor depends on the extrinsic curvature of the brane.

hep-th↗
arXiv2012

Ultraviolet-infrared mixing on the noncommutative Minkowski space in the Yang-Feldman formalism

We study infrared divergences due to ultraviolet-infrared mixing in quantum field theory on Moyal space with Lorentzian signature in the Yang-Feldman formalism. Concretely, we are considering the phi^4 and the phi^3 model in arbitrary even dimension. It turns out that the situation is worse than in the Euclidean setting, in the sense that we find infrared divergences in graphs that are finite there. We briefly discuss the problems one faces when trying to adapt the nonlocal counterterms that render the Euclidean model renormalizable.

hep-th↗