Comments on M24_{24} representations and CY3CY_3 geometries

We show using string dualities that Mathieu moonshine controls Gromov-Witten invariants and periods of the holomorphic 3-form $\Omega$ 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.Comment: 27 pages, v2: minor additions, published versio

Twisted Supergravity and Koszul Duality: A Case Study in AdS₃

In this note, we study a simplified variant of the familiar holographic duality between supergravity on AdS₃ × S³ × T⁴ and the SCFT (on the moduli space of) the symmetric orbifold theory Sym^N(T⁴) as N→∞. 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→∞ limit of the twisted gravitational theory. We emphasize the role of 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

A fast and reliable method for the delineation of tree crown outlines for the computation of crown openness values and other crown parameters

Numerous crown parameters (e.g., leaf area index, diameter, height, volume) can be obtained via the analysis of tree crown photographs. In all cases, parameter values are functions of the position of the crown outline. However, no standardized method to delineate crowns exists. To explore the effect of different outlines on tree crown descriptors, in this case crown openness (CO), and facilitate the adoption of a standard method free of user bias, we developed the program Crown Delineator that automatically delineates any outline around tree crowns following predetermined sensibility settings. We used different outlines to analyze tree CO in contrasting settings: using saplings from four species in young boreal mixedwood forests and medium-sized hybrid poplar trees from a low-density plantation. In both cases, the estimated CO increases when calculated from a looser outline, which had a strong influence on understory available light simulations using a forest simulator. These results demonstrate that the method used to trace crown outlines is an important step in the determination of CO values. We provide a much-needed computer-assisted solution to help standardize this procedure, which can also be used in many other situations in which the delineation of tree crowns is needed (e.g., competition and crown shyness)

No more walls! A tale of modularity, symmetry, and wall crossing for 1/4 BPS dyons

Abstract We determine the generating functions of 1/4 BPS dyons in a class of 4d N $$\mathcal{N}$$ = 4 string vacua arising as CHL orbifolds of K3 × 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

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.Comment: 19 pages, 2 figure

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.Comment: 73 pages, with results summarized in introduction. v2: added a discussion about coupling to gravity (section 3.3), additional references, minor corrections and improvement

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.Comment: 22 pages, 3 tables. We thank T. Eguchi and K. Hikami for permission to copy our Tables 2 and 3 (M24 character table and q-expansions of some twining genera in the (4,4) sigma model with K3 target) from their article arXiv:1008.492

Heterotic sigma models on T8T^8 and the Borcherds automorphic form Φ12\Phi_{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 $\Phi_{12}$, 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.Comment: 12 pages; v2 error (involving fermion zero modes) correcte

Junior Faculty Engagement at iSchools: Personal Experience during the First Several Years

This roundtable discussion will explore how junior faculty at iSchools have been able to embed their research, teaching, and service activities within their schools, the larger institutions, and broader communities. The session will also focus on the ways in which junior faculty have received guidance in their roles--from the job search through the first several years in a tenure-track position. Roundtable leaders represent a variety of institutions and experiences--as faculty at the University of Illinois at Urbana-Champaign [WJM], the University of Maryland [SP], the University of North Carolina at Chapel Hill [PME], and the University of Texas at Austin [MW], and with doctoral-level preparation at the University of North Carolina at Chapel Hill [WJM, MW], the University of Toronto [SP], and the University of Washington [PME]. While the annual junior faculty mentoring event at the iConference specifically targets junior faculty as participants, this roundtable session offers a more inclusive environment for the discussion of this topic, specifically engaging doctoral students and senior faculty as well as their junior colleagues