Searcharxiv⌕ Search

arXiv subjects

Jan de Boer

Publications and source records attributed to Jan de Boer.

At least 145 records · Page 8Linked to original sources
arXiv1998

Six-Dimensional Supergravity on S^3 X AdS_3 and 2d Conformal Field Theory

In this paper we study the relation between six-dimensional supergravity compactified on S^3 X AdS_3 and certain two-dimensional conformal field theories. We compute the Kaluza-Klein spectrum of supergravity using representation theory; these methods are quite general and can also be applied to other compactifications involving anti-de Sitter spaces. A detailed comparison between the spectrum of the two-dimensional conformal field theory and supergravity is made, and we find complete agreement. This applies even at the level of certain non-chiral primaries, and we propose a resolution to the puzzle of the missing states recently raised by Vafa. As a further illustration of the method the Kaluza-Klein spectra of F-theory on M^6 X S^3 X AdS_3 and of M-theory on M^6 X S^2 X AdS_3 are computed, with M^6 some Calabi-Yau manifold.

hep-th↗
arXiv1998

Conformal Field Theories: From Old to New

In a short review of recent work, we discuss the general problem of constructing the actions of new conformal field theories from old conformal field theories. Such a construction follows when the old conformal field theory admits new conformal stress tensors in its chiral algebra, and it turns out that the new conformal field theory is generically a new spin-two gauge theory. As an example we discuss the new spin-two gauged sigma models which arise in this fashion from the general conformal non-linear sigma model.

hep-th↗
arXiv1998

New Spin-Two Gauged Sigma Models and General Conformal Field Theory

Recently, we have studied the general Virasoro construction at one loop in the background of the general non-linear sigma model. Here, we find the action formulation of these new conformal field theories when the background sigma model is itself conformal. In this case, the new conformal field theories are described by a large class of new spin-two gauged sigma models. As examples of the new actions, we discuss the spin-two gauged WZW actions, which describe the conformal field theories of the generic affine-Virasoro construction, and the spin-two gauged g/h coset constructions. We are able to identify the latter as the actions of the local Lie h-invariant conformal field theories, a large class of generically irrational conformal field theories with a local gauge symmetry.

hep-th↗
arXiv1998

Membrane Scattering in Curved Space with M-Momentum Transfer

We study membrane scattering in a curved space with non-zero M-momentum p_{11} transfer. In the low-energy short-distance region, the membrane dynamics is described by a three-dimensional N=4 supersymmetric gauge theory. We study an n-instanton process of the gauge theory, corresponding to the exchange of n units of p_{11}, and compare the result with the scattering amplitude computed in the low-energy long-distance region using supergravity. We find that they behave differently. We show that this result is not in contradiction with the large-N Matrix Theory conjecture, by pointing out that cutoff scales of the supergravity and the gauge theory are complementary to each other.

hep-th↗
arXiv1998

Branes and Dynamical Supersymmetry Breaking

We study dynamical supersymmetry breaking in four dimensions using the fivebrane of M theory, in particular for the Izawa-Yanagida-Intriligator-Thomas (IYIT) model, which we realize as the worldvolume theory of a certain M-theory fivebrane configuration. From the brane point of view, supersymmetry is broken when a holomorphic configuration with the proper boundary conditions does not exist. We discuss the difference between explicit and spontaneous supersymmetry breaking and between runaway behavior and having a stable vacuum. As a preparation for the study of the IYIT model, we examine a realization of the orientifold four-plane in M theory. We derive known as well as new results on the moduli spaces of N=2 and N=1 theories with symplectic gauge groups. These results are based on a hypothesis that a certain intersection of the fivebrane and the Z_2 fixed plane breaks supersymmetry. In the IYIT model, we show that the brane exhibits runaway behavior when the flavor group is gauged. On the other hand, if the flavor group is not gauged, we find that the brane does not run away. We suggest that a stable supersymmetry-breaking vacuum is realized in the region beyond the reach of the supergravity approximation.

hep-th↗
arXiv1997

Kahler Potential and Higher Derivative Terms from M Theory Fivebrane

The construction of four dimensional supersymmetric gauge theories via the fivebrane of M theory wrapped around a Riemann surface has been successfully applied to the computation of holomorphic quantities of field theory. In this paper we compute non-holomorphic quantities in the eleven dimensional supergravity limit of M theory. While the Kahler potential on the Coulomb of N=2 theories is correctly reproduced, higher derivative terms in the N=2 effective action differ from what is expected for the four dimensional gauge theory. For the Kahler potential of N=1 theories at an abelian Coulomb phase, the result again differs from what is expected for the four-dimensional gauge theory. Using a gravitational back reaction method for the fivebrane we compute the metric on the Higgs branch of N=2 gauge theories. Here we find an agreement with the results expected for the gauge theories. A similar computation of the metric on N=1 Higgs branches yields information on the complex structure associated with the flavor rotation in one case and the classical metric in another. We discuss what four-dimensional field theory quantities can be computed via the fivebrane in the supergravity limit of M theory.

hep-th↗
arXiv1997

Monopole Condensation and Confining Phase of N=1 Gauge Theories Via M Theory Fivebrane

The fivebrane of M theory is used in order to study the moduli space of vacua of confining phase N=1 supersymmetric gauge theories in four dimensions. The supersymmetric vacua correspond to the condensation of massless monopoles and confinement of photons. The monopole and meson vacuum expectation values are computed using the fivebrane configuration. The comparison of the fivebrane computation and the field theory analysis shows that at vacua with a classically enhanced gauge group SU(r) the effective superpotential obtained by the "integrating in" method is exact for r=2 but is not exact for r > 2. The fivebrane configuration corresponding to N=1 gauge theories with Landau-Ginzburg type superpotentials is studied. N=1 non-trivial fixed points are analyzed using the brane geometry.

hep-th↗
arXiv1997

Dynamics of N=2 Supersymmetric Gauge Theories in Three Dimensions

We study the structure of the moduli spaces of vacua and superpotentials of N=2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N=2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N_c) and SU(N_c) with N_f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.

hep-th↗
arXiv1997

Branes and Mirror Symmetry in N=2 Supersymmetric Gauge Theories in Three Dimensions

We use brane configurations and SL(2,Z) symmetry of the type IIB string to construct mirror N=2 supersymmetric gauge theories in three dimensions. The mirror map exchanges Higgs and Coulomb branches, Fayet-Iliopoulos and mass parameters and U(1)R symmetries. Some quantities that are determined at the quantum level in one theory are determined at the classical level of the mirror. One such example is the complex structure of the Coulomb branch of one theory which is determined quantum mechanically. It is mapped to the complex structure of the Higgs branch of the mirror theory, which is determined classically. We study the generation of N=2 superpotentials by open D-string instantons in the brane configurations.

hep-th↗
arXiv1996

Mirror Symmetry in Three-Dimensional Gauge Theories, SL(2,Z) and D-Brane Moduli Spaces

We construct intersecting D-brane configurations that encode the gauge groups and field content of dual N=4 supersymmetric gauge theories in three dimensions. The duality which exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters is derived from the SL(2,Z) symmetry of the type IIB string. Using the D-brane configurations we construct explicitly this mirror map between the dual theories and study the instanton corrections in the D-brane worldvolume theory via open string instantons. A general procedure to obtain mirror pairs is presented and illustrated. We encounter transitions among different field theories that correspond to smooth movements in the D-brane moduli space. We discuss the relation between the duality of the gauge theories and the level-rank duality of affine Lie algebras. Examples of other dual theories are presented and explained via T-duality and extremal transitions in type II string compactifications. Finally we discuss a second way to study instanton corrections in the gauge theory, by wrapping five-branes around six-cycles in M-theory compactified on a Calabi-Yau 4-fold.

hep-th↗
arXiv1996

Wakimoto realizations of current algebras: an explicit construction

A generalized Wakimoto realization of $\widehat{\cal G}_K$ can be associated with each parabolic subalgebra ${\cal P}=({\cal G}_0 +{\cal G}_+)$ of a simple Lie algebra ${\cal G}$ according to an earlier proposal by Feigin and Frenkel. In this paper the proposal is made explicit by developing the construction of Wakimoto realizations from a simple but unconventional viewpoint. An explicit formula is derived for the Wakimoto current first at the Poisson bracket level by Hamiltonian symmetry reduction of the WZNW model. The quantization is then performed by normal ordering the classical formula and determining the required quantum correction for it to generate $\widehat{\cal G}_K$ by means of commutators. The affine-Sugawara stress-energy tensor is verified to have the expected quadratic form in the constituents, which are symplectic bosons belonging to ${\cal G}_+$ and a current belonging to ${\cal G}_0$. The quantization requires a choice of special polynomial coordinates on the big cell of the flag manifold $P\backslash G$. The effect of this choice is investigated in detail by constructing quantum coordinate transformations. Finally, the explicit form of the screening charges for each generalized Wakimoto realization is determined, and some applications are briefly discussed.

hep-th↗
arXiv1996

Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes

We construct and analyze dual N=4 supersymmetric gauge theories in three dimensions with unitary and symplectic gauge groups. The gauge groups and the field content of the theories are encoded in quiver diagrams. The duality exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters. We analyze the classical and the quantum moduli spaces of the theories and construct an explicit mirror map between the mass parameters and the the Fayet-Iliopoulos parameters of the dual. The results generalize the relation between ALE spaces and moduli spaces of SU(n) and SO(2n) instantons. We interpret some of these results from the string theory viewpoint, for SU(n) by analyzing T-duality and extremal transitions in type II string compactifications, for SO(2n) by using D-branes as probes. Finally, we make a proposal for the moduli space of vacua of these theories in the absence of matter.

hep-th↗
arXiv1996

Target Space Supersymmetric Sigma Model Calculations

We briefly review the covariant formulation of the Green-Schwarz superstring by Berkovits, and describe how a detailed tree-level and one-loop analysis of this model leads, for the first time, to a derivation of the low-energy effective action of the heterotic superstring while keeping target-space supersymmetry manifest. The resulting low-energy theory is old-minimal supergravity coupled to tensor multiplet. The dilaton is part of the compensator multiplet.

hep-th↗
arXiv1996

Covariant Computation of the Low Energy Effective Action of the Heterotic Superstring

We derive the low energy effective action of the heterotic superstring in superspace. This is achieved by coupling the covariantly quantized Green-Schwarz superstring of Berkovits to a curved background and requiring that the sigma model has superconformal invariance at tree level and at one loop in $\a'$. Tree level superconformal invariance yields the complete supergravity algebra, and one-loop superconformal invariance the equations of motion of the low energy theory. The resulting low energy theory is old-minimal supergravity coupled to a tensor multiplet. The dilaton is part of the compensator multiplet.

hep-th↗
arXiv1996

An explicit construction of Wakimoto realizations of current algebras

It is known from a work of Feigin and Frenkel that a Wakimoto type, generalized free field realization of the current algebra $\widehat{\cal G}_k$ can be associated with each parabolic subalgebra ${\cal P}=({\cal G}_0+{\cal G}_+)$ of the Lie algebra ${\cal G}$, where in the standard case ${\cal G}_0$ is the Cartan and ${\cal P}$ is the Borel subalgebra. In this letter we obtain an explicit formula for the Wakimoto realization in the general case. Using Hamiltonian reduction of the WZNW model, we first derive a Poisson bracket realization of the ${\cal G}$-valued current in terms of symplectic bosons belonging to ${\cal G}_+$ and a current belonging to ${\cal G}_0$. We then quantize the formula by determining the correct normal ordering. We also show that the affine-Sugawara stress-energy tensor takes the expected quadratic form in the constituents.

hep-th↗
arXiv1995

The equivalence between the operator approach and the path integral approach for quantum mechanical non-linear sigma models

We give background material and some details of calculations for two recent papers [1,2] where we derived a path integral representation of the transition element for supersymmetric and nonsupersymmetric nonlinear sigma models in one dimension (quantum mechanics). Our approach starts from a Hamiltonian $H(\hat{x}, \hat{p}, \hatψ, \hatψ^\dagger)$ with a priori operator ordering. By inserting a finite number of complete sets of $x$ eigenstates, $p$ eigenstates and fermionic coherent states, we obtain the discretized path integral and the discretized propagators and vertices in closed form. Taking the continuum limit we read off the Feynman rules and measure of the continuum theory which differ from those often assumed. In particular, mode regularization of the continuum theory is shown in an example to give incorrect results. As a consequence of time-slicing, the action and Feynman rules, although without any ambiguities, are necessarily noncovariant, but the final results are covariant if $\hat{H}$ is covariant. All our derivations are exact. Two loop calculations confirm our results.

hep-th↗
arXiv1995

Loop calculations in quantum-mechanical non-linear sigma models sigma models with fermions and applications to anomalies

We construct the path integral for one-dimensional non-linear sigma models, starting from a given Hamiltonian operator and states in a Hilbert space. By explicit evaluation of the discretized propagators and vertices we find the correct Feynman rules which differ from those often assumed. These rules, which we previously derived in bosonic systems \cite{paper1}, are now extended to fermionic systems. We then generalize the work of Alvarez-Gaumé and Witten \cite{alwi} by developing a framework to compute anomalies of an $n$-dimensional quantum field theory by evaluating perturbatively a corresponding quantum mechanical path integral. Finally, we apply this formalism to various chiral and trace anomalies, and solve a series of technical problems: $(i)$ the correct treatment of Majorana fermions in path integrals with coherent states (the methods of fermion doubling and fermion halving yield equivalent results when used in applications to anomalies), $(ii)$ a complete path integral treatment of the ghost sector of chiral Yang-Mills anomalies, $(iii)$ a complete path integral treatment of trace anomalies, $(iv)$ the supersymmetric extension of the Van Vleck determinant, and $(v)$ a derivation of the spin-$3\over 2$ Jacobian of Alvarez-Gaumé and Witten for Lorentz anomalies.

hep-th↗