Monstrous BPS-algebras and the superstring origin of moonshine

Paquette, Natalie M.; Persson, Daniel; Volpato, Roberto

doi:10.4310/cntp.2016.v10.n3.a2

Cited by 43 publications

(114 citation statements)

References 63 publications

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“…In Section 4, we derived a representation of some of the Niemeier lattices in the free fermionic formulation. The properties of 24-dimensional lattices and their moonshine symmetries are of growing interest in the literature [69][70][71][72][73][74][75][76]. In this context, it is not implausible that the free fermionic methods can add to the set of tools that can be used to explore the underlying mathematical structures.…”

Section: Discussionmentioning

confidence: 99%

Niemeier Lattices in the Free Fermionic Heterotic–String Formulation

Athanasopoulos

Faraggi

2017

Advances in Mathematical Physics

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The spinor-vector duality was discovered in free fermionic constructions of the heterotic string in four dimensions. It played a key role in the construction of heterotic-string models with an anomaly-free extra symmetry that may remain unbroken down to low energy scales. A generic signature of the low scale string derived model is via diphoton excess that may be within reach of the LHC. A fascinating possibility is that the spinor-vector duality symmetry is rooted in the structure of the heterotic-string compactifications to two dimensions. The two-dimensional heterotic-string theories are in turn related to the so-called moonshine symmetries that underlie the two-dimensional compactifications. In this paper, we embark on exploration of this connection by the free fermionic formulation to classify the symmetries of the two-dimensional heterotic-string theories. We use two complementary approaches in our classification. The first utilises a construction which is akin to the one used in the spinor-vector duality. Underlying this method is the triality property of (8) representations. In the second approach, we use the free fermionic tools to classify the twenty-four-dimensional Niemeier lattices.

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Section: Discussionmentioning

confidence: 99%

Niemeier Lattices in the Free Fermionic Heterotic–String Formulation

Athanasopoulos

Faraggi

2017

Advances in Mathematical Physics

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“…• Matrices with n 2 = 0 mod N can be decomposed as 29) for the tensor integral, and • Charges (Q, P) such that p = 0 mod N are in the same orbit as purely electric charges (Q, 0).…”

Section: Trivial Orbitmentioning

confidence: 99%

Four-derivative couplings and BPS dyons in heterotic CHL orbifolds

2017

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Three-dimensional string models with half-maximal supersymmetry are believed to be invariant under a large U-duality group which unifies the S and T dualities in four dimensions. We propose an exact, U-duality invariant formula for four-derivative scalar couplings of the form F (Φ) (∇Φ) 4 in a class of string vacua known as CHL Z N heterotic orbifolds with N prime, generalizing our previous work which dealt with the case of heterotic string on T 6 . We derive the Ward identities that F (Φ) must satisfy, and check that our formula obeys them. We analyze the weak coupling expansion of F (Φ), and show that it reproduces the correct treelevel and one-loop contributions, plus an infinite series of non-perturbative contributions. Similarly, the large radius expansion reproduces the exact F 4 coupling in four dimensions, including both supersymmetric invariants, plus infinite series of instanton corrections from half-BPS dyons winding around the large circle, and from Taub-NUT instantons. The summation measure for dyonic instantons agrees with the helicity supertrace for half-BPS dyons in 4 dimensions in all charge sectors. In the process we clarify several subtleties about CHL models in D = 4 and D = 3, in particular we obtain the exact helicity supertraces for 1/2-BPS dyonic states in all duality orbits.

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“…3 The orbifold action kills the extra zero modes, but leaves the left-moving sector untouched. The ground-state degeneracy of the right-movers gives an overall factor of 24, as in [15]. Including this degeneracy, the result (for a given N ) is…”

Section: Basic Connectionmentioning

confidence: 86%

“…The factor of 24 again arises from the right-moving ground state degeneracy, as in [15]. We see that there is a precise analogy to the findings in [1,2]: just as an (automorphic correction of)…”

Section: Second Quantizationmentioning

confidence: 87%

“…One can circumvent this vanishing by inserting powers of F in the trace to soak up zero modes, as in [14]; however, this will alter the modularity properties and spoil the connection we intend to make to Φ 12 . Instead, we consider, following [15], a 'twisted' computation where we trace over left-moving excitations but consider the ground states of the Z 2 orbifold of the right-moving sector -that is, we consider the right-movers to live in the Ramond sector of the Conway module constructed by Duncan [16]. 3 The orbifold action kills the extra zero modes, but leaves the left-moving sector untouched.…”

Section: Basic Connectionmentioning

confidence: 99%

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Heterotic sigma models on T 8 and the Borcherds automorphic form Φ12

Harrison

Kachru

Paquette

et al. 2017

J. High Energ. Phys.

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Abstract: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; Z). We comment on possible implications for Umbral moonshine and theories of AdS 3 gravity.

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Monstrous BPS-algebras and the superstring origin of moonshine

Cited by 43 publications

References 63 publications

Niemeier Lattices in the Free Fermionic Heterotic–String Formulation

Niemeier Lattices in the Free Fermionic Heterotic–String Formulation

Four-derivative couplings and BPS dyons in heterotic CHL orbifolds

Heterotic sigma models on T 8 and the Borcherds automorphic form Φ12

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