arXiv subjects

Melanie Becker

Publications and source records attributed to Melanie Becker.

At least 19 recordsLinked to original sources

arXiv2020

Five-dimensional Supergravity in N = 1/2 Superspace

We construct 5D, N = 1 supergravity in a 4D, N = 1 superspace with an extra bosonic coordinate. This represents four of the supersymmetries and the associated Poincaré symmetries manifestly. The remaining four supersymmetries and the rest of the Poincaré symmetries are represented linearly but not manifestly. In the linearized approximation, the action reduces to the known superspace result. As an application of the formalism, we construct the $\int A\wedge R\wedge R$ invariant in this superspace.

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arXiv2018

N=1 Supercurrents of Eleven-dimensional Supergravity

Eleven-dimensional supergravity can be formulated in superspaces locally of the form $\mathbf X\times Y$ where $\mathbf X$ is 4D $N=1$ conformal superspace and $Y$ is an arbitrary 7-manifold admitting a $G_2$-structure. The eleven-dimensional 3-form and the stable 3-form on $Y$ define the lowest component of a gauge superfield on $\mathbf X \times Y$ that is chiral as a superfield on $\mathbf X$. This chiral field is part of a tensor hierarchy giving rise to a superspace Chern-Simons action and its real field strength defines a lifting of the Hitchin functional on $Y$ to the $G_2$ superspace $\mathbf X\times Y$. These terms are those of lowest order in a superspace Noether expansion in seven $N=1$ conformal gravitino superfields $Ψ$. In this paper, we compute the $O(Ψ)$ action to all orders in the remaining fields. The eleven-dimensional origin of the resulting non-linear structures is parameterized by the choice of a complex spinor on $Y$ encoding the off-shell 4D $N=1$ subalgebra of the eleven-dimensional super-Poincare algebra.

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arXiv2017

Conformal interfaces between free boson orbifold theories

We construct a large class of conformal interfaces between two-dimensional c=1 conformal field theories describing compact free bosons and their Z_2 orbifolds. The interfaces are obtained by constructing boundary states in the corresponding c=2 product theories and applying the unfolding procedure. We compute the fusion products for all of these defects, and identify the invertible topological interfaces associated to global symmetries, the interfaces corresponding to marginal deformations, and the interfaces which map the untwisted sector of an orbifold to the invariant states of the parent theory.

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arXiv2017

Eleven-Dimensional Supergravity in 4D, $N=1$ Superspace

We give a formulation of linearized 11D supergravity in 4D, $N=1$ superspace keeping all eleven bosonic coordinates. The fields are fluctuations around $\mathbf M=\mathbf R^{4|4}\times Y$, where $Y$ is a background Riemannian 7-manifold admitting a $G_2$ structure. We embed the 11D fields into superfield representations of the 4D, $N=1$ superconformal algebra. These consist of the conformal graviton superfield, seven conformal gravitino superfields, a tensor hierarchy of superfields describing the 11D 3-form, and a non-abelian Kaluza-Klein vector multiplet gauging the tensor hierarchy by diffeomorphisms on $Y$. The quadratic action consists of the linearization of a superspace volume term and a Chern-Simons action for the gauged hierarchy coupled to the supergravity and gravitino superfields, and the full structure is fixed by superconformal and gauge invariance. When this action is projected to components, we recover the full linearized action of 11D supergravity.

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arXiv2017

M-theory Potential from the $G_2$ Hitchin Functional in Superspace

We embed the component fields of eleven-dimensional supergravity into a superspace of the form $X\times Y$ where $X$ is the standard 4D, $N=1$ superspace and $Y$ is a smooth 7-manifold. The eleven-dimensional 3-form gives rise to a tensor hierarchy of superfields gauged by the diffeomorphisms of $Y$. It contains a natural candidate for a $G_2$ structure on $Y$, and being a complex of superforms, defines a superspace Chern-Simons invariant. Adding to this a natural generalization of the Riemannian volume on $X\times Y$ and freezing the (superspin-$\frac32$ and 1) supergravity fields on $X$, we obtain an approximation to the eleven-dimensional supergravity action that suffices to compute the scalar potential. In this approximation the action is the sum of the superspace Chern-Simons term and a superspace generalization of the Hitchin functional for $Y$ as a $G_2$-structure manifold. Integrating out auxiliary fields, we obtain the conditions for unbroken supersymmetry and the scalar potential. The latter reproduces the Einstein-Hilbert term on $Y$ in a form due to Bryant.

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arXiv2017

All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies

We give a geometric description of supersymmetric gravity/(non-)abelian $p$-form hierarchies in superspaces with 4D, $N = 1$ super-Poincare invariance. These hierarchies give rise to Chern-Simons-like invariants, such as those of the 5D, $N = 1$ graviphoton and the eleven-dimensional 3-form but also generalizations such as Green-Schwarz-like/BF-type couplings. Previous constructions based on prepotential superfields are reinterpreted in terms of $p$-forms in superspace thereby elucidating the underlying geometry. This vastly simplifies the calculations of superspace field-strengths, Bianchi identities, and Chern-Simons invariants. Using this, we prove the validity of a recursive formula for the conditions defining these actions for any such tensor hierarchy. Solving it at quadratic and cubic orders, we recover the known results for the BF-type and cubic Chern-Simons actions. As an application, we compute the quartic invariant $\sim A dA dA dA + \ldots$ relevant, for example, to seven-dimensional supergravity compactifications.

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arXiv2017

Defects and boundary RG flows in $\mathbb{C}/\mathbb{Z}_d$

We show that topological defects in the language of Landau-Ginzburg models carry information about the RG flow between the non-compact orbifolds $\mathbb{C}/\mathbb{Z}_d$. We show that such defects correctly implement the bulk-induced RG flow on the boundary.

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arXiv2016

Some tree-level string amplitudes in the NSR formalism

We calculate tree level scattering amplitudes for open strings using the NSR formalism. We present a streamlined symmetry-based and pedagogical approach to the computations, which we first develop by checking two-, three-, and four-point functions involving bosons and fermions. We calculate the five-point amplitude for massless gluons and find agreement with an earlier result by Brandt, Machado and Medina. We then compute the five-point amplitudes involving two and four fermions respectively, the general form of which has not been previously obtained in the NSR formalism. The results nicely confirm expectations from the supersymmetric $F^4$ effective action. Finally we use the prescription of Kawai, Lewellen and Tye (KLT) to compute the amplitudes for the closed string sector.

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arXiv2016

Chern-Simons Actions and Their Gaugings in 4D, N=1 Superspace

We gauge the abelian hierarchy of tensor fields in 4D by a Lie algebra. The resulting non-abelian tensor hierarchy can be interpreted via an equivariant chain complex. We lift this structure to N=1 superspace by constructing superfield analogs for the tensor fields, along with covariant superfield strengths. Next we construct Chern-Simons actions, for both the bosonic and N=1 cases, and note that the condition of gauge invariance can be presented cohomologically. Finally, we provide an explicit realization of these structures by dimensional reduction, for example by reducing the three-form of eleven-dimensional supergravity into a superspace with manifest 4D, N=1 supersymmetry.

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arXiv2016

Abelian Tensor Hierarchy in 4D, N=1 Superspace

With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) tensor hierarchy of p-forms in four-dimensional, N=1 superspace and construct its Chern-Simons-like invariants. When specialized to the case in which the tensors arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N=1 superfields.

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arXiv2016

Three-Point Disc Amplitudes in the RNS Formalism

We calculate all tree level string theory vacuum to Dp-brane disc amplitudes involving an arbitrary RR-state and two NS-NS vertex operators. This computation was earlier performed by K. Becker, Guo, and Robbins for the simplest case of a RR-state of type C_{p-3}. Here we use the aid of a computer to calculate all possible three-point amplitudes involving a RR-vertex operator of type C_{p+1+2k}.

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arXiv2015

The alpha'-Expansion of Calabi-Yau Compactifications

We consider alpha'-corrections to Calabi-Yau compactifications of type II string theory. These were discussed from the string worldsheet approach many years ago in terms of supersymmetric non-linear sigma-models by Nemeschansky and Sen as well as Gross and Witten. There it was shown that once alpha'-corrections are included, the internal manifold solving the string equations of motion is still Calabi-Yau though not Ricci flat. In this brief note we review these results and compare with a space-time effective field theory approach, in which we show that SU(3)-holonomy manifolds become SU(3)-structure manifolds once such corrections are included.

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arXiv2015

M-theory and G_2 Manifolds

In this talk we report on recent progress in describing compactifications of string theory and M-theory on G_2 and Spin(7) manifolds. We include the infinite set of alpha'-corrections and describe the entire tower of massless and massive Kaluza-Klein modes resulting from such compactifications.

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arXiv2015

String Corrected Spacetimes and SU(N)-Structure Manifolds

Using an effective field theory approach and the language of SU(N)-structures, we study higher derivative corrections to the supersymmetry constraints for compactifications of string or M-theory to Minkowski space. Our analysis is done entirely in the target space and is thus very general, and does not rely on theory-dependent details such as the amount of worldsheet supersymmetry. For manifolds of real dimension n<4 we show that the internal geometry remains flat and uncorrected. For n=4, 6, Kahler manifolds with SU(N)-holonomy can become corrected to SU(N)-structure, while preserving supersymmetry, once corrections are included.

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arXiv2014

Kaluza-Klein Theories Without Truncation

In this note we present a closed expression for the space-time effective action for all bosonic fields (massless and massive) obtained from the compactification of gravity or supergravity theories (such as type II or eleven-dimensional supergravities) from $D$ to $d$ space-time dimensions.

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arXiv2014

Finite-temperature three-point function in 2D CFT

We calculate the finite temperature three-point correlation function for primary fields in a 2D conformal field theory in momentum space. This result has applications to any strongly coupled field theory with a 2D CFT dual, as well as to Kerr/CFT.

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arXiv2012

Boundary Terms, Spinors and Kerr/CFT

Similarly as in AdS/CFT, the requirement that the action for spinors be stationary for solutions to the Dirac equation with fixed boundary conditions determines the form of the boundary term that needs to be added to the standard Dirac action in Kerr/CFT. We determine this boundary term and make use of it to calculate the two-point function for spinor fields in Kerr/CFT. This two-point function agrees with the correlator of a two dimensional relativistic conformal field theory.

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arXiv2010

Extremal Three-point Correlators in Kerr/CFT

We compute three-point correlation functions in the near-extremal, near-horizon region of a Kerr black hole, and compare to the corresponding finite-temperature conformal field theory correlators. For simplicity, we focus on scalar fields dual to operators ${\cal O}_h$ whose conformal dimensions obey $h_3=h_1+h_2$, which we name \emph{extremal} in analogy with the classic $AdS_5 \times S^5$ three-point function in the literature. For such extremal correlators we find perfect agreement with the conformal field theory side, provided that the coupling of the cubic interaction contains a vanishing prefactor $\propto h_3-h_1-h_2$. In fact, the bulk three-point function integral for such extremal correlators diverges as $1/(h_3-h_1-h_2)$. This behavior is analogous to what was found in the context of extremal AdS/CFT three-point correlators. As in AdS/CFT our correlation function can nevertheless be computed via analytic continuation from the non-extremal case.

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