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P. van Nieuwenhuizen

Publications and source records attributed to P. van Nieuwenhuizen.

At least 19 recordsLinked to original sources
arXiv2009

Quantum corrections to solitons and BPS saturation

We review our work of the past decade on one-loop quantum corrections to the mass M and central charge Z of solitons in supersymmetric field theories: the kink, the vortex, and the monopoles (focussing on the kink and the monopoles here). In each case a new feature was needed to obtain BPS saturation: a new anomaly-like contribution to Z for the kink and the N=2 monopole, the effect of classical winding of the quantum vortex contributing to Z, surface terms contributing to M of the N=4 monopole and to Z of the N=2 and N=4 monopoles, and composite operator renormalization for the currents of the "finite" N=4 model. We use dimensional regularization, modified to preserve susy and be applicable to solitons, and suitable renormalization conditions. In the mode expansion of bosonic and fermionic quantum fields, zero modes appear then as massless nonzero modes.

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arXiv2007

Consistent boundary conditions for supergravity

We derive the complete orbit of boundary conditions for supergravity models which is closed under the action of all local symmetries of these models, and which eliminates spurious field equations on the boundary. We show that the Gibbons-Hawking boundary conditions break local supersymmetry if one imposes local boundary conditions on all fields. Nonlocal boundary conditions are not ruled out. We extend our analysis to BRST symmetry and to the Hamiltonian formulation of these models.

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arXiv2006

Boundary Terms in Supergravity and Supersymmetry

We begin with the simplest possible introduction to supergravity. Then we discuss its spin 3/2 stress tensor; these results are new. Next, we discuss boundary conditions on fields and boundary actions for N=1 supergravity. Finally, we discuss new boundary contributions to the mass and central charge of monopoles in N=4 super Yang-Mills theory. All models are in 3+1 dimensions.

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arXiv2005

BPS saturation of the N=4 monopole by infinite composite-operator renormalization

Quantum corrections to the magnetic central charge of the monopole in N=4 supersymmetric Yang-Mills theory are free from the anomalous contributions that were crucial for BPS saturation of the two-dimensional supersymmetric kink and the N=2 monopole. However these quantum corrections are nontrivial and they require infinite renormalization of the supersymmetry current, central charges, and energy-momentum tensor, in contrast to N=2 and even though the N=4 theory is finite. Their composite-operator renormalization leads to counterterms which form a multiplet of improvement terms. Using on-shell renormalization conditions the quantum corrections to the mass and the central charge then vanish both, thus verifying quantum BPS saturation.

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arXiv2004

N=4 Superconformal Symmetry for the Covariant Quantum Superstring

We extend our formulation of the covariant quantum superstring as a WZNW model with N=2 superconformal symmetry to N=4. The two anticommuting BRST charges in the N=4 multiplet of charges are the usual BRST charge Q_S and a charge Q_V proposed by Dijkgraaf, Verlinde and Verlinde for topological models. Using our recent work on "gauging cosets", we then construct a further charge Q_C which anticommutes with Q_S + Q_V and which is intended for the definition of the physical spectrum.

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arXiv2004

A new anomalous contribution to the central charge of the N=2 monopole

We calculate the one-loop corrections to the mass and central charge of the BPS monopole in N=2 super-Yang-Mills theory in 3+1 dimensions using a supersymmetry-preserving version of dimensional regularization adapted to solitons. In the renormalization scheme where previous studies have indicated vanishing quantum corrections, we find nontrivial corrections that we identify as the 3+1 dimensional analogue of the anomaly in the conformal central charge of the N=1 supersymmetric kink in 1+1 dimensions. As in the latter case, the associated contribution to the ordinary central charge has exactly the required magnitude to preserve BPS saturation at the one-loop level. It also restores consistency of calculations involving sums over zero-point energies with the low-energy effective action of Seiberg and Witten.

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arXiv2004

Gauging Cosets

We show how to gauge the set of raising and lowering generators of an arbitrary Lie algebra. We consider SU(N) as an example. The nilpotency of the BRST charge requires constraints on the ghosts associated to the raising and lowering generators. To remove these constraints we add further ghosts and we need a second BRST charge to obtain nontrivial cohomology. The second BRST operator yields a group theoretical explanation of the grading encountered in the covariant quantization of superstrings.

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arXiv2004

Harmonic Superspaces from Superstrings

We derive harmonic superspaces for N=2,3,4 SYM theory in four dimensions from superstring theory. The pure spinors in ten dimensions are dimensionally reduced and yield the harmonic coordinates. Two anticommuting BRST charges implement Grassmann analyticity and harmonic analyticity. The string field theory action produces the action and field equations for N=3 SYM theory in harmonic superspace.

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arXiv2004

Superstrings and WZNW Models

We give a brief review of our approach to the quantization of superstrings. New is a covariant derivation of the measure at tree level and a path integral formula for this measure.

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arXiv2004

The Casimir effect for susy solitons

We discuss new insights into the quantum physics of solitons developed since 1997: why quantum corrections to the mass M and the central charge Z of solitons in supersymmetric (susy) field theories in 1+1 and 2+1 dimensions are nonvanishing, despite the fact that the zero-point energies of bosons and fermions seem to cancel each other, and the central charge is an integral of a total space derivative which naively seems to get contributions only from regions far removed from the soliton. Crucial are: (1) the requirement that the regularization scheme not only makes calculations finite, but it also should preserve (ordinary) supersymmetry, (2) the renormalization condition that tadpoles vanish in the trivial vacuum, (3) an anomaly in the central charge which is actually needed to saturate the Bogomolnyi bound, (4) the influence of the winding of classical fields on the quantum fields far away from the soliton.

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arXiv2003

An Introduction to the Covariant Quantization of Superstrings

We give an introduction to a new approach to the covariant quantization of superstrings. After a brief review of the classical Green--Schwarz superstring and Berkovits' approach to its quantization based on pure spinors, we discuss our covariant formulation without pure spinor constraints. We discuss the relation between the concept of grading, which we introduced to define vertex operators, and homological perturbation theory, and we compare our work with recent work by others. In the appendices, we include some background material for the Green-Schwarz and Berkovits formulations, in order that this presentation be self contained.

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arXiv2003

Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation

The one-loop quantum corrections to the mass and central charge of the N=2 vortex in 2+1 dimensions are determined using supersymmetry-preserving dimensional regularization by dimensional reduction of the corresponding N=1 model with Fayet-Iliopoulos term in 3+1 dimensions. Both the mass and the central charge turn out to have nonvanishing one-loop corrections which however are equal and thus saturate the Bogomolnyi bound. We explain BPS saturation by standard multiplet shortening arguments, correcting a previous claim in the literature postulating the presence of a second degenerate short multiplet at the quantum level.

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arXiv2003

The Quantum Superstring as a WZNW Model with N=2 Superconformal Symmetry

We present a new development in our approach to the covariant quantization of superstrings in 10 dimensions which is based on a gauged WZNW model. To incorporate worldsheet diffeomorphisms we need the quartet of ghosts $(b_{zz},c^{z}, \b_{zz}, \g^{z})$ for topological gravity. The currents of this combined system form an N=2 superconformal algebra. The model has vanishing central charge and contains two anticommuting BRST charges, $Q_{S}=Q_{W} + \oint \g^{z} b_{zz} + \oint η_{z}$ and $Q_{V} = \oint c^{z} \Big(T^{W}_{zz} + {1\over 2} T^{top}_{zz}\Big) + \g^{z} (B^{W}_{zz} + {1\over 2} B^{top}_{zz} \Big)$, where $η_{z}$ is obtained by the usual fermionization of $\b_{zz}, \g^{z}$. Physical states form the cohomology of $Q_{S}+Q_{V}$, have nonnegative grading, and are annihilated by $b_{0}$ and $β_{0}$. We no longer introduce any ghosts by hand, and the formalism is completely Lorentz covariant.

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arXiv2003

Non-commutative superspace from string theory

Turning on background fields in string theory sometimes has an alternative interpretation as a deformation of the target space geometry. A particularly well-known case is the NS-NS two form B, which gives rise to space-time non-commutativity. In this note we point out that this phenomenon extends to ten-dimensional superspace when employing a covariant quantization of the superstring, generalizing an observation by Ooguri and Vafa in four dimensions. In particular, we will find that RR field strengths give rise to a non-zero $\{θ,θ\}$ anti-commutator, just as in four dimensions, whereas the gravitino yields a non-zero value for $[x,θ]$.

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arXiv2002

Quantum corrections to the mass and central charge of solitons in 1+1 dimensions

We first discuss how the longstanding confusion in the literature concerning one-loop quantum corrections to 1+1 dimensional solitons has finally been resolved. Then we use 't Hooft and Veltman's dimensional regularization to compute the kink mass, and find that chiral domain wall fermions, induced by fermionic zero modes, lead to spontaneous parity violation and an anomalous contribution to the central charge such that the BPS bound becomes saturated. On the other hand, Siegel's dimensional reduction shifts this anomaly to the counter terms in the renormalized current multiplet. The superconformal anomaly is located in an evanescent counter term, and imposing supersymmetry, this counter term induces the same anomalous contribution to the central charge. Next we discuss a new regularization scheme: local mode regularization. The local energy density computed in this scheme satisfies the BPS equality (it is equal to the local central charge density). In an appendix we give a very detailed account of the DHN method to compute soliton masses applied to the supersymmetric kink.

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arXiv2002

Heat kernels and zeta-function regularization for the mass of the supersymmetric kink

We apply zeta-function regularization to the kink and susy kink and compute its quantum mass. We fix ambiguities by the renormalization condition that the quantum mass vanishes as one lets the mass gap tend to infinity while keeping scattering data fixed. As an alternative we write the regulated sum over zero point energies in terms of the heat kernel and apply standard heat kernel subtractions. Finally we discuss to what extent these procedures are equivalent to the usual renormalization conditions that tadpoles vanish.

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arXiv2002

Comment on `One Loop Renormalization of Soliton Quantum Mass Corrections in 1+1 Dimensional Scalar Field Theory Models' (Phys. Lett. B542 (2002) 282 [hep-th/0206047])

We refute the claim that previous works on the one-loop quantum mass of solitons had incorrectly dropped a surface term from a partial integration. Rather, the paper quoted in the title contains a fallacious derivation with two compensating errors. We also remark that the $ϕ^2\cos^2\ln(ϕ^2)$ model considered in that paper does not have solitons at the quantum level because at two-loop order the degeneracy of the vacua is lifted. This may be remedied, however, by a supersymmetric extension.

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