arXiv subjects

Natalie M. Paquette

Publications and source records attributed to Natalie M. Paquette.

36 records · Page 2Linked to original sources

arXiv2020

Twisted Supergravity and Koszul Duality: A case study in AdS$_3$

In this note, we study a simplified variant of the familiar holographic duality between supergravity on AdS$_3\times S^3\times T^4$ and the SCFT (on the moduli space of) the symmetric orbifold theory $Sym^N(T^4)$ as $N \rightarrow \infty$. This variant arises conjecturally from a twist proposed by the first author and Si Li. We recover a number of results concerning protected subsectors of the original duality working directly in the twisted bulk theory. Moreover, we identify the symmetry algebra arising in the $N\rightarrow \infty$ limit of the twisted gravitational theory. We emphasize the role of $\textit{Koszul duality}$---a ubiquitous mathematical notion to which we provide a friendly introduction---in field theory and string theory. After illustrating the appearance of Koszul duality in the "toy" example of holomorphic Chern-Simons theory, we describe how (a deformation of) Koszul duality relates bulk and boundary operators in our twisted setup, and explain how one can compute algebra OPEs diagrammatically using this notion. Further details, results, and computations will appear in a companion paper.

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arXiv2019

Flux vacua: A voluminous recount

In this note we apply mathematical results for the volume of certain symmetric spaces to the problem of counting flux vacua in simple IIB Calabi--Yau compactifications. In particular we obtain estimates for the number of flux vacua including the geometric factor related to the Calabi-Yau moduli space, in the large flux limit, for the FHSV model and some closely related models. We see that these geometric factors give rise to contributions to the counting formula that are typically not of order one and might potentially affect the counting qualitatively in some cases. We also note, for simple families of Calabi-Yau moduli spaces, an interesting dependence of the moduli space volumes on the dimension of the flux space, which in turn is governed by the Betti numbers of the Calabi-Yaus.

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arXiv2019

(0,2) Dualities and the 4-Simplex

We propose that a simple, Lagrangian 2d $\mathcal{N}=(0, 2)$ duality interface between the 3d $\mathcal{N}=2$ XYZ model and 3d $\mathcal{N}=2$ SQED can be associated to the simplest triangulated 4-manifold: the 4-simplex. We then begin to flesh out a dictionary between more general triangulated 4-manifolds with boundary and 2d $\mathcal{N}=(0, 2)$ interfaces. In particular, we identify IR dualities of interfaces associated to local changes of 4d triangulation, governed by the (3,3), (2,4), and (4,2) Pachner moves. We check these dualities using supersymmetric half-indices. We also describe how to produce stand-alone 2d theories (as opposed to interfaces) capturing the geometry of 4-simplices and Pachner moves by making additional field-theoretic choices, and find in this context that the Pachner moves recover abelian $\mathcal{N}=(0,2)$ trialities of Gadde-Gukov-Putrov. Our work provides new, explicit tools to explore the interplay between 2d dualities and 4-manifold geometry that has been developed in recent years.

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arXiv2018

A Borcherds-Kac-Moody superalgebra with Conway symmetry

We construct a Borcherds Kac-Moody (BKM) superalgebra on which the Conway group Co$_0$ acts faithfully. We show that the BKM algebra is generated by the BRST-closed states in a chiral superstring theory. We use this construction to produce denominator identities for the chiral partition functions of the Conway module $V^{s\natural}$, a supersymmetric $c=12$ chiral conformal field theory whose (twisted) partition functions enjoy moonshine properties and which has automorphism group isomorphic to Co$_0$. In particular, these functions satisfy a genus zero property analogous to that of monstrous moonshine. Finally, we suggest how one may promote the denominators to spacetime BPS indices in type II string theory, which might thus furnish a physical explanation of the genus zero property of Conway moonshine.

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arXiv2018

Dual Boundary Conditions in 3d SCFT's

We propose matching pairs of half-BPS boundary conditions related by IR dualities of 3d $\mathcal{N}=2$ gauge theories. From these matching pairs we construct duality interfaces. We test our proposals by anomaly matching and the computation of supersymmetric indices. Examples include basic abelian dualities, level-rank dualities, and Aharony dualities.

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arXiv2017

Landau-Ginzburg Orbifolds and Symmetries of K3 CFTs

Recent developments in the study of the moonshine phenomenon, including umbral and Conway moonshine, suggest that it may play an important role in encoding the action of finite symmetry groups on the BPS spectrum of K3 string theory. To test and clarify these proposed K3-moonshine connections, we study Landau-Ginzburg orbifolds that flow to conformal field theories in the moduli space of K3 sigma models. We compute K3 elliptic genera twined by discrete symmetries that are manifest in the UV description, though often inaccessible in the IR. We obtain various twining functions coinciding with moonshine predictions that have not been observed in physical theories before. These include twining functions arising from Mathieu moonshine, other cases of umbral moonshine, and Conway moonshine. For instance, all functions arising from $M_{11} \subset 2.M_{12}$ moonshine appear as explicit twining genera in the LG models, which moreover admit a uniform description in terms of its natural 12-dimensional representation. Our results provide strong evidence for the relevance of umbral moonshine for K3 symmetries, as well as new hints for its eventual explanation.

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arXiv2017

Heterotic sigma models on $T^8$ and the Borcherds automorphic form $Φ_{12}$

We consider the spectrum of BPS states of the heterotic sigma model with $(0,8)$ supersymmetry and $T^8$ target, as well as its second-quantized counterpart. We show that the counting function for such states is intimately related to Borcherds' automorphic form $Φ_{12}$, a modular form which exhibits automorphy for $O(2,26;{\mathbb Z})$. We comment on possible implications for Umbral moonshine and theories of AdS$_3$ gravity.

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arXiv2017

No More Walls! A Tale of Modularity, Symmetry, and Wall Crossing for 1/4 BPS Dyons

We determine the generating functions of 1/4 BPS dyons in a class of 4d $\mathcal{N}=4$ string vacua arising as CHL orbifolds of $K3 \times T^2$, a classification of which has been recently completed. We show that all such generating functions obey some simple physical consistency conditions that are very often sufficient to fix them uniquely. The main constraint we impose is the absence of unphysical walls of marginal stability: discontinuities of 1/4 BPS degeneracies can only occur when 1/4 BPS dyons decay into pairs of 1/2 BPS states. Formally, these generating functions in spacetime can be described as multiplicative lifts of certain supersymmetric indices (twining genera) on the worldsheet of the corresponding nonlinear sigma model on K3. As a consequence, our procedure also leads to an explicit derivation of almost all of these twining genera. The worldsheet indices singled out in this way match precisely a set of functions of interest in moonshine, as predicted by a recent conjecture.

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arXiv2017

BPS Algebras, Genus Zero, and the Heterotic Monster

In this note, we expand on some technical issues raised in \cite{PPV} by the authors, as well as providing a friendly introduction to and summary of our previous work. We construct a set of heterotic string compactifications to 0+1 dimensions intimately related to the Monstrous moonshine module of Frenkel, Lepowsky, and Meurman (and orbifolds thereof). Using this model, we review our physical interpretation of the genus zero property of Monstrous moonshine. Furthermore, we show that the space of (second-quantized) BPS-states forms a module over the Monstrous Lie algebras $\mathfrak{m}_g$---some of the first and most prominent examples of Generalized Kac-Moody algebras---constructed by Borcherds and Carnahan. In particular, we clarify the structure of the module present in the second-quantized string theory. We also sketch a proof of our methods in the language of vertex operator algebras, for the interested mathematician.

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arXiv2016

3D String Theory and Umbral Moonshine

The simplest string theory compactifications to 3D with 16 supercharges -- the heterotic string on $T^7$, and type II strings on $K3 \times T^3$ -- are related by U-duality, and share a moduli space of vacua parametrized by $O(8,24; \mathbb{Z}) \backslash O(8,24) / (O(8) \times O(24))$. One can think of this as the moduli space of even, self-dual 32-dimensional lattices with signature (8,24). At 24 special points in moduli space, the lattice splits as $Γ^{8,0} \oplus Γ^{0,24}$. $Γ^{0,24}$ can be the Leech lattice or any of 23 Niemeier lattices, while $Γ^{8,0}$ is the $E_8$ root lattice. We show that starting from this observation, one can find a precise connection between the Umbral groups and type IIA string theory on $K3$. This provides a natural physical starting point for understanding Mathieu and Umbral moonshine. The maximal unbroken subgroups of Umbral groups in 6D (or any other limit) are those obtained by starting at the associated Niemeier point and moving in moduli space while preserving the largest possible subgroup of the Umbral group. To illustrate the action of these symmetries on BPS states, we discuss the computation of certain protected four-derivative terms in the effective field theory, and recover facts about the spectrum and symmetry representations of 1/2-BPS states.

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arXiv2016

Emergent space-time and the supersymmetric index

It is of interest to find criteria on a 2d CFT which indicate that it gives rise to emergent gravity in a macroscopic 3d AdS space via holography. Symmetric orbifolds in the large $N$ limit have partition functions which are consistent with an emergent space-time string theory with $L_{\rm string} \sim L_{\rm AdS}$. For supersymmetric CFTs, the elliptic genus can serve as a sensitive probe of whether the SCFT admits a large radius gravity description with $L_{\rm string} \ll L_{\rm AdS}$ after one deforms away from the symmetric orbifold point in moduli space. We discuss several classes of constructions whose elliptic genera strongly hint that gravity with $L_{\rm Planck} \ll L_{\rm string} \ll L_{\rm AdS}$ can emerge at suitable points in moduli space.

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arXiv2016

Monstrous BPS-Algebras and the Superstring Origin of Moonshine

We provide a physics derivation of Monstrous moonshine. We show that the McKay-Thompson series $T_g$, $g\in \mathbb{M}$, can be interpreted as supersymmetric indices counting spacetime BPS-states in certain heterotic string models. The invariance groups of these series arise naturally as spacetime T-duality groups and their genus zero property descends from the behaviour of these heterotic models in suitable decompactification limits. We also show that the space of BPS-states forms a module for the Monstrous Lie algebras $\mathfrak{m}_g$, constructed by Borcherds and Carnahan. We argue that $\mathfrak{m}_g$ arise in the heterotic models as algebras of spontaneously broken gauge symmetries, whose generators are in exact correspondence with BPS-states. This gives $\mathfrak{m}_g$ an interpretation as a kind of BPS-algebra.

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arXiv2015

On the elliptic genera of manifolds of Spin(7) holonomy

Superstring compactification on a manifold of Spin(7) holonomy gives rise to a 2d worldsheet conformal field theory with an extended supersymmetry algebra. The $\mathcal{N}=1$ superconformal algebra is extended by additional generators of spins 2 and 5/2, and instead of just superconformal symmetry one has a $c=12$ realization of the symmetry group $\mathcal{SW}(3/2,2)$. In this paper, we compute the characters of this supergroup, and decompose the elliptic genus of a general Spin(7) compactification in terms of these characters. We find suggestive relations to various sporadic groups, which are made more precise in a companion paper.

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arXiv2015

Elliptic Genera and 3d Gravity

We describe general constraints on the elliptic genus of a 2d supersymmetric conformal field theory which has a gravity dual with large radius in Planck units. We give examples of theories which do and do not satisfy the bounds we derive, by describing the elliptic genera of symmetric product orbifolds of $K3$, product manifolds, certain simple families of Calabi-Yau hypersurfaces, and symmetric products of the "Monster CFT." We discuss the distinction between theories with supergravity duals and those whose duals have strings at the scale set by the AdS curvature. Under natural assumptions we attempt to quantify the fraction of (2,2) supersymmetric conformal theories which admit a weakly curved gravity description, at large central charge.

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arXiv2015

Towards a Holographic Bose-Hubbard Model

We present a holographic construction of the large-N Bose-Hubbard model. The model is based on Maxwell fields coupled to charged scalar fields on the AdS2 hard wall. We realize the lobe-shaped phase structure of the Bose-Hubbard model and find that the model admits Mott insulator ground states in the limit of large Coulomb repulsion. In the Mott insulator phases, the bosons are localized on each site. At zero hopping we find that the transitions between Mott insulating phases with different fillings correspond to first order level-crossing phase transitions. At finite hopping we find a holographic phase transition between the Mott phase and a non-homogeneous phase. We then analyze the perturbations of fields around both the Mott insulator phase and inhomogeneous phase. We find almost zero modes in the non-homogeneous phase.

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arXiv2014

Comments on M$_{24}$ representations and $CY_3$ geometries

We show using string dualities that Mathieu moonshine controls Gromov-Witten invariants and periods of the holomorphic 3-form $Ω$ for certain $CY_3$ manifolds. We also discuss how the period vectors appear in flux compactifications on these $CY_3$ manifolds and work out the connection between the sporadic group M$_{24}$ and the Yukawa couplings in four dimensional theories that arise from heterotic string theory compactifications on these $CY_3$ manifolds.

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arXiv2013

Twining Genera of (0,4) Supersymmetric Sigma Models on K3

Conformal field theories with (0,4) worldsheet supersymmetry and K3 target can be used to compactify the E8xE8 heterotic string to six dimensions in a supersymmetric manner. The data specifying such a model includes an appropriate configuration of 24 gauge instantons in the E8xE8 gauge group to satisfy the constraints of anomaly cancellation. In this note, we compute twining genera - elliptic genera with appropriate insertions of discrete symmetry generators in the trace - for (0,4) theories with various instanton embeddings. We do this by constructing linear sigma models which flow to the desired conformal field theories, and using the techniques of localization. We present several examples of such twining genera which are consistent with a moonshine relating these (0,4) models to the finite simple sporadic group M24.

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arXiv2013

Universal scaling function for the two-dimensional Ising model in an external field: A pragmatic approach

We report an effective functional form for the spin-spin correlation function of the 2D Ising model as a function of temperature and field. Although the Ising model has been well studied, no analytical result for the spin-spin correlation function exists for arbitrary magnetic fields and temperatures. We show the validity of our form by comparison with simulations using the Wolff algorithm, and obtain remarkable precision by including analytic corrections to scaling. Given recent interest in comparing biomembrane heterogeneity to Ising criticality, our spin-spin correlation function may be used as a predictive quantitative measure for FRET or NMR membrane experiments.

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