Dyon degeneracies from Mathieu moonshine symmetry

We provide strong evidence that a large number of CY 3 manifolds are involved in an intricate way in Mathieu moonshine viz. their Gromov-Witten invariants are related to the expansion coefficients of the twined/twisted-twined elliptic genera of K3. We use the conjectured string duality between CHL orbifolds of heterotic string theory on K3 × T 2 and type IIA string theory on CY 3 manifolds to explicitly show this connection. We then work out two concrete examples where we exactly match the expansion coefficients on both sides of the duality.

“…the McKay-Thompson series. This was studied explicitly for the compactifications of the heterotic E 8 × E 8 string theory on K3 × T 2 in [12,14,15].…”

Section: Introductionmentioning

confidence: 99%

On Mathieu moonshine and Gromov-Witten invariants

Banlaki

Chowdhury

Kidambi

et al. 2020

“…We adapt the proof of [10] for configurations with magnetic charge P 2 = 2 and demonstrate that the index is positive. We then extend this observation to all the CHL models and to other orbifolds associated with Mathieu moonshine introduced in [11,12].…”

Section: Jhep03(2021)106mentioning

confidence: 72%

“…In [11,13] it was observed that for N = 4 models obtained by freely acting Z 2 , Z 3 orbifolds of type IIB on T 6 , the index for single centered configurations after factorising…”

Section: Jhep03(2021)106mentioning

confidence: 99%

“…The trace is performed over the Ramond-Ramond sector of the N = (4, 4) super conformal field theory of K3 with (c,c) = (6, 6), F is the Fermion number and j is the left moving U(1) charge of the SU(2) R-symmetry of K3. The twisted elliptic genera for the g corresponding to conjugacy classes of M 23 ∪ M 24 have been evaluated in [11]. These take the form…”

Section: Horizon States For the 1/4 Bps Dyonmentioning

confidence: 99%

See 1 more Smart Citation

Horizon states and the sign of their index in $$ \mathcal{N} $$ = 4 dyons

Chattopadhyaya

David

2021

Self Cite

Classical single centered solutions of 1/4 BPS dyons in $$ \mathcal{N} $$ N = 4 theories are usually constructed in duality frames which contain non-trivial hair degrees of freedom localized outside the horizon. These modes are in addition to the fermionic zero modes associated with broken supersymmetry. Identifying and removing the hair from the 1/4 BPS index allows us to isolate the degrees of freedom associated with the horizon. The spherical symmetry of the horizon then ensures that index of the horizon states has to be positive. We verify that this is indeed the case for the canonical example of dyons in type IIB theory on K3 × T2 and prove this property holds for a class of states. We generalise this observation to all CHL orbifolds, this involves identifying the hair and isolating the horizon degrees of freedom. We then identify the horizon states for 1/4 BPS dyons in $$ \mathcal{N} $$ N = 4 models obtained by freely acting ℤ2 and ℤ3 orbifolds of type IIB theory compactified on T6 and observe that the index is again positive for single centred black holes. This observation coupled with the fact the 1/4 BPS index of single centred solutions without removal of the hair violates positivity indicates that there exists no duality frame in these models without non-trivial hair.

“…For example, it was shown in [30] that the Gromov-Witten invariants of certain CY 3 manifolds are connected to Mathieu moonshine. This was further explored and studied in [31][32][33][34][35].…”

Section: Jhep02(2018)129mentioning

confidence: 99%

Calabi-Yau manifolds and sporadic groups

Banlaki

Chowdhury

Kidambi

et al. 2018

A few years ago a connection between the elliptic genus of the K3 manifold and the largest Mathieu group M 24 was proposed. We study the elliptic genera for Calabi-Yau manifolds of larger dimensions and discuss potential connections between the expansion coefficients of these elliptic genera and sporadic groups. While the Calabi-Yau 3-fold case is rather uninteresting, the elliptic genera of certain Calabi-Yau d-folds for d > 3 have expansions that could potentially arise from underlying sporadic symmetry groups. We explore such potential connections by calculating twined elliptic genera for a large number of Calabi-Yau 5-folds that are hypersurfaces in weighted projected spaces, for a toroidal orbifold and two Gepner models.