Fricke S-duality in CHL models

Persson, Daniel; Volpato, Roberto

doi:10.1007/jhep12(2015)156

Cited by 34 publications

(102 citation statements)

References 70 publications

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“…The lattice Λ m is tabulated in the sixth column of Table 1, taken from [18]. It agrees with the result (2.2) upon making use of the lattice isomorphisms (A.33).…”

Section: ) Where G Pq ≡ O(p Q)/[o(p)×o(q)]supporting

confidence: 78%

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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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“…The lattice Λ m is tabulated in the sixth column of Table 1, taken from [18]. It agrees with the result (2.2) upon making use of the lattice isomorphisms (A.33).…”

Section: ) Where G Pq ≡ O(p Q)/[o(p)×o(q)]supporting

confidence: 78%

“…In [18] it was observed that the coupling (2.3) is in fact invariant under the larger group Γ 0 (N ), obtained by adjoining to Γ 0 (N ) the Fricke involution, which acts on modular forms of weight k…”

Section: ) Where G Pq ≡ O(p Q)/[o(p)×o(q)]mentioning

confidence: 99%

Four-derivative couplings and BPS dyons in heterotic CHL orbifolds

2017

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“…The twining genus Z g is directly related to the generating function 1/ g of the degeneracies of 1/4 BPS dyons in this CHL model [20,[29][30][31][32]35,36,67,84]. Up to dualities, the CHL model only depends on the Frame shape of g [80]. This is apparently puzzling for those Frame shapes that correspond to multiple O + ( 4,20 )-classes and therefore to multiple twining genera Z g : In these cases, there are different candidates 1/ g for the 1/4 BPS-counting function, one for each distinct twining genus…”

Section: Discussionmentioning

confidence: 99%

“…(see, e.g., [51] or [80] for a proof). On the other hand, the only possible Witten indices of an N = (4, 4) SCFT with central charge 6 and integer U (1) charges are 0 or 24 [75].…”

Section: Modular Groups and Multipliersmentioning

confidence: 99%

K3 string theory, lattices and moonshine

Cheng

Harrison²,

Volpato

et al. 2018

Res Math Sci

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In this paper, we address the following two closely related questions. First, we complete the classification of finite symmetry groups of type IIA string theory on K 3 × R 6 , where Niemeier lattices play an important role. This extends earlier results by including points in the moduli space with enhanced gauge symmetries in spacetime, or, equivalently, where the world-sheet CFT becomes singular. After classifying the symmetries as abstract groups, we study how they act on the BPS states of the theory. In particular, we classify the conjugacy classes in the T-duality group O + ( 4,20 ) which represent physically distinct symmetries. Subsequently, we make two conjectures regarding the connection between the corresponding twining genera of K 3 CFTs and Conway and umbral moonshine, building upon earlier work on the relation between moonshine and the K 3 elliptic genus.

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“…The arithmetic Hecke groups appear for Z N orbifolds with N = 1, 2, 3, and 4, which correspond in turn to the Hecke groups with heights 3, 4, 6, and ∞ respectively. In fact, there exists a wider class of CHL models whose S-duality group contains the Fricke involution τ → − 1 N τ , in addition to the subgroup of SL(2, Z) [48]. Among them, those which are called self-dual are invariant under the Fricke involution.…”

Section: Supersymmetric Gauge Theoriesmentioning

confidence: 99%

Aspects of Hecke Symmetry:Anomalies, Curves, and Chazy Equations

Ashok

Jatkar²,

Raman³

2020

SIGMA

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Motivated by their appearance in supersymmetric gauge and string theories, we study the relations governing quasi-automorphic forms associated to certain discrete subgroups of SL(2, R) called Hecke groups. The Eisenstein series associated to a Hecke group H(m) satisfy a set of m coupled linear differential equations, which are natural analogues of the well-known Ramanujan identities for modular forms of SL(2, Z). We prove these identities by appealing to a correspondence with the generalized Halphen system. Each Hecke group is then associated to a (hyper-)elliptic curve, whose coefficients are found to be determined by an anomaly equation. The Ramanujan identities admit a natural geometrical interpretation as a vector field on the moduli space of this curve. They also allow us to associate a non-linear differential equation of order m to each Hecke group. These equations are higher-order analogues of the Chazy equation, and we show that they are solved by the quasi-automorphic Eisenstein series E 2 associated to H(m) and its Hecke orbits. We conclude by demonstrating that these non-linear equations possess the Painlevé property.

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Fricke S-duality in CHL models

Cited by 34 publications

References 70 publications

Four-derivative couplings and BPS dyons in heterotic CHL orbifolds

Four-derivative couplings and BPS dyons in heterotic CHL orbifolds

K3 string theory, lattices and moonshine

Aspects of Hecke Symmetry:Anomalies, Curves, and Chazy Equations

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