Both objects arise naturally in a conformal vertex algebra v the jfunction as the character and the monster as the automorphism group. The first twentyfive years twentyfive years ago, conway and norton published in this journal their remarkable paper monstrous moonshine. The symmetries of any given shape have a natural sort of arithmetic to them. You should not miss their eccentric proposal of relating bells theorem to the baby monster group. Monstrous lie algebras research on finite groups title. Monstrous moonshine conway 1979 bulletin of the london. Monstrous moonshine describes the unexpected relation between the modular jfunction and the largest sporadic simple group known as the monster. Please join the simons foundation and our generous member organizations in supporting arxiv during our giving campaign september 2327. Department of pure mathematics and mathematical statistics, university of cambridge, 16 mill lane, cambridge cb2 1sb. The symmetry twisted partition functions exhibit the celebrated monstrous moonshine phenomenon. Your comment will not appear until it has been approved by the creator. He also found my posts on a talk i gave on monstrous moonshine for 2nd year students earlier this.
Monstrous moonshine from orbifolds tuite, michael p. We outline a proof of the fact that most cases nortonsof generalized moonshine conjecture for twisted. Dec 20, 2004 a part of our presentation is a rigorous definition of conformal field theory following segals axioms, and some examples, such as lattice theories associated with a unimodular even lattice. Vertex algebras and string theory in monstrous moonshine. Monstrous moonshine describes the unexpected relation between the modular j function and the largest sporadic simple group known as the. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks. Such formulas are dictated by the structure of the graded monstrous moonshine modules. It also precipitated monstrous moonshine, which is an appearance of monster symmetry in number theory that catalysed developments in. We argue that the monster cft has a kramerswannier duality defect that is not associated with any global symmetry.
Monstrous moonshine relates distinguished modular functions to the representation theory of the monster. We show that the main conway and norton monstrous moonshine properties, stating that the thompson series for each monster group conjugacy class has a modular invariance group of genus zero, follow from an orbifold construction based on an orbifold. Carlos can still remember the day he decided he wanted to be a teacher. Download it once and read it on your kindle device, pc, phones or tablets. Twentyfive years ago, conway and norton published in this journal their remarkable paper monstrous moonshine, proposing a completely unexpected relationship between finite simple groups and modular functions. Monstrous moonshine is probably one of the most esoteric achievements arising in mathematics. Scottcarnahan we describe a generalization borcherdssof two constructions of the monster lie algebra byproducing,foreach element of the monster simple group, a pair in. C this article has been rated as cclass on the projects quality scale. In mathematics, monstrous moonshine, or moonshine theory, is a term devised by john. We also include certain examples and formulate conjectures on modular forms and monstrous moonshine related to the present work. This is an expository talk on the monstrous moonshine conjectures about the monster simple group in mathematics. Pdf sketch of a program for universal automorphic functions. Twentyfive years ago, conway and norton published in this journal their remarkable paper monstrous moonshine, proposing a completely unexpected re we use cookies to enhance your experience on our website.
We consider the monster module of frenkel, lepowsky, and meurman as az 2 orbifold of a bosonic string compactified by the leech lattice. Detailed quotes explanations with page numbers for every important quote on the site. Captures moonshine vapor and funnels it to the condenser. Monstrous moonshine bulletin of the london mathematical society. It is by construction clear that the underlying conformal field the ory is a k3 sigmamodel describing string propagation. Norton in 1979, used to describe the unexpected connection between the monster group m and modular functions, in particular, the j function. Moonshine the first quarter century and beyond proceedings of a workshop on the moonshine conjectures and vertex algebras orell fussli. Mid this article has been rated as midpriority on the. The monstrous moonshine conjecture is an outrageous idea that stemmed from an observation made by john mckay of concordia university in 1978. Ashfaque 1 monstrous moonshine moonshine remains a mysterious relationship between natural objects from two distinct realms of math ematics.
Norton in 1979, used to describe the unexpected connection. An approach to establishing the genus zero property of monstrous moonshine via quantum gravity is discussed in 29. Nov 21, 2020 in mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group m and modular functions, in particular, the j function. The fact that the monster has connections to other parts of mathematics shows that there is something very deep going on here. Towards strengthening the analogy between umbral and monstrous moonshine, we reframe mathieu moonshine by repackaging the mathieu moonshine mock modular forms in a few different ways, verifying the existence of corresponding modules, and giving. Monstrous moonshine refers to the surprising relationship, discovered in the 1970s, between a certain function called the jfunction and the largest finite simple group of order 1054, called the monster group. By continuing to use our website, you are agreeing to our use of cookies. By 1980, the classification of simple finite groups was in sight.
In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group m and modular functions, in particular, the j function. We shall use this fact to give a simple description of the normalise0rn of i tn psl2u which does not seem to be generally known. This article is a short and elementary introduction to the monstrous moonshine aiming to be as accessible as possible. Mathematicians chase moonshine, string theory connections.
Etd connections between mock modular forms and vertex. It is now known that lying behind monstrous moonshine is a certain conformal field theory having the monster group. Sidebar collapsible in mathematics, monstrous moonshine, or moonshine theory, is a term devised by john conway and simon p. A quick summary of the recent amazing discoveries about the fischergriess. We argue that the monster cft has a kramerswannier duality defect that is not associated with any. In mathematics, monstrous moonshine, or moonshine theory, is a term devised by john conway and simon p. Thompson series for each monster group conjugacy class has a modular. Pdf downloads of all 1427 litcharts literature guides, and of every new one we publish. Monstrous moonshine and the uniqueness of the moonshine. These monstrous moonshine observations connected the fields of number theory and group theory in an unforeseen way. Norton in 1979 it is now known that lying behind monstrous moonshine is a vertex operator algebra called the moonshine module or monster vertex algebra constructed by igor. Hed grown up in a household where following the family line was expected, particularly because he was the only son. Moonshine is a relation between nite groups and modular objects.
Pdf a short introduction to monstrous moonshine researchgate. While the story relating the monstrous moonshine to a particular 2d cft is beautiful to be sure, it has seemed a peculiarity until 2010 when k3 entered the story. Decompositions of the moonshine module with respect to. The study of this relation started with the socalled monstrous moonshine 22 and has recently been revived by the discovery of mathieu moonshine 12,35,36,41,42 and umbral moonshine 17,18, which recovers mathieu moonshine as a special case. Monstrous moonshine wikimili, the best wikipedia reader. Monstrous moonshine and monstrous lie superalgebras. Conformal field theory and elliptic cohomology sciencedirect. Journal of algebra 115, 501512 1988 generalized kacmoody algebras richard borcherds department qf pure mathematics and mathematical sratistics. In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group m and modular functions, in particular. The coils allow the alcohol vapor to cool into your liquid moonshine.
Mckay was leafing through a table of abstruse mathematical data, giving possible values for coefficients of the j function of certain elliptic curves, when he noticed the number 196,884 in the expression. Monstrous moonshine relates distinguished modular functions to the representation theory of the monster m. From a modern point of view, topological defects generalize the notion of global symmetries. Recent works in moonshine suggest deep relations between number theory and physics. Later, part of the monstrous moonshine observation was explained via the construction, due to frenkel, lepowsky, and meurman flm, of a certain twodimensional conformal field theory or vertex operator algebra.
This article is within the scope of wikiproject mathematics, a collaborative effort to improve the coverage of mathematics on wikipedia. Towards strengthening the analogy between umbral and monstrous moonshine, we reframe mathieu moonshine by repackaging the mathieu moonshine mock modular forms in a few different ways, verifying the existence of corresponding modules, and giving various applications including connections with arithmetic. A starting point in the theory of moonshine is the 1979 paper of j. Moonshine, the monster, conformal field theory, and elliptic cohomology have all been linked. Their hyperbolic polygons show a considerable singularity cusp. King lear act 2, scene 2 translation shakescleare, by. This works creator has chosen to moderate comments on the work. Monstrous moonshine, bulletin of the london mathematical society, volume 11, issue 3, 1 october 1979, pages 308339, we use cookies to enhance your experience on our website. Teacher editions with classroom activities for all 1427 titles we cover. The pot belly holds your mash, is placed on the heat source and sends the vapor moonshine to the onion top. A resolution for standard modules of borcherds lie algebras. Monstrous moonshine bulletin of the london mathematical. Number theoretic kloosterman sums have reappeared in quantum gravity, and mock modular forms have emerged as candidates for the computation of black hole degeneracies.
View the article pdf and any associated supplements and figures for a period of 48 hours. The study of this relation started with the socalled monstrous moonshine 22 and has recently been revived by the discovery of mathieu moonshine 12,35,36,41,42 and umbral moonshine 17,18, which recovers mathieu moonshine. This paper is an introduction to the monstrous moonshine correspondence aiming at an undergraduate level. We determine the space of 1point correlation functions associated with the moonshine module. While the story relating the monstrous moonshine to a particular 2d cft is beautiful to. Moonshine topic of research paper in physical sciences. It collects several seemingcoincidences about how the then conjectural monster group, along with other sporadic nite simple groups like the mathieu groups, relate to modular forms. Pdf this paper is an introduction to the monstrous moonshine correspondence aiming at an undergraduate level. Metrics details download to read the full article text.
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