On symmetries of N $$ \mathcal{N} $$ = (4, 4) sigma models on T 4

Volpato, Roberto

doi:10.1007/jhep08(2014)094

Cited by 21 publications

(21 citation statements)

References 68 publications

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“…(9.12)), for some N, for all choices of and g ∈ G . Moreover, φ g is found to coincide with the g-twined K3 elliptic genus associated to the sigma model defined by , for all the examples computed in [109,113,228]. (These examples account for about half of the conjugacy classes of Co 0 that fix a 4-space in ⊗ Z R.) In particular, taking g = e in (9.37) recovers the K3 elliptic genus (9.4), but in the form 38) where 24 .…”

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confidence: 75%

Moonshine

Duncan

Griffin

Ono

2015

Mathematical Sciences

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illustrate the case of J(τ ) = j(τ ) − 744, whose coefficients turn out to be sums of the dimensions of the 194 irreducible representations of M. Such formulas are dictated by the structure of the graded monstrous moonshine modules. Recent works in moonshine suggest deep relations between number theory and physics. Number theoretic Kloosterman sums have reappeared in quantum gravity, and mock modular forms have emerged as candidates for the computation of black hole degeneracies. This paper is a survey of past and present research on moonshine. We also compute the quantum dimensions of the monster orbifold and obtain exact formulas for the multiplicities of the irreducible components of the moonshine modules. These formulas imply that such multiplicities are asymptotically proportional to dimensions.

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confidence: 75%

Moonshine

Duncan

Griffin

Ono

2015

Mathematical Sciences

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“…The only relevant cases are (r L , r R ) = (0, 1/2) and (r L , r R ) = (0, 1/3), in which cases L is the D 4 or A 2 2 root lattices, respectively (see [90] for more details). In particular, the untwined elliptic genus of T 4 is Z e (T 4 ; τ , z) = 0.…”

Section: Torus Orbifoldsmentioning

confidence: 99%

“…The relevant values of r L , r R and the Frame shapes of the corresponding quantum symmetries are collected in Table 1 (see [90]). A set of more general twining genera can be obtained as follows.…”

Section: Torus Orbifoldsmentioning

confidence: 99%

“…It is not difficult to compute the twining genus of a quantum symmetry, since it can be computed from the twining genus of g on the NLSM T T 4 on the T 4 . In [90], general formulas for the twining genera of all possible symmetries of any NLSM on T 4 were given. The supersymmetric NLSM on T 4 has four left-moving and four right-moving Majorana-Weyl fermions.…”

Section: Torus Orbifoldsmentioning

confidence: 99%

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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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“…either only a lift of order four exists, or there are invariant charge vectors whose associated momentum-winding fields are multiplied by (−1). The latter phenomenon of "non-trivial phases" is compatible with the description of symmetries of toroidal sigma models [19], and it had been taken into account in previous discussions of symmetries in conformal field theory [18,19,33]. The former phenomenon, which affects the relevant groups of symmetries, has not been discussed in this form before.…”

Section: Introductionmentioning

confidence: 98%

Not doomed to fail

Taormina

Wendland

2018

J. High Energ. Phys.

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In their recent manuscript "An Uplifting Discussion of T-Duality", 1707.08888, J. Harvey and G. Moore have reevaluated a mod two condition appearing in asymmetric orbifold constructions as an obstruction to the description of certain symmetries of toroidal conformal field theories by means of automorphisms of the underlying charge lattice. The relevant "doomed to fail" condition determines whether or not such a lattice automorphism g may lift to a symmetry in the corresponding toroidal conformal field theory without introducing extra phases. If doomed to fail, then in some cases, the lift of g must have double the order of g. It is an interesting question, whether or not "geometric" symmetries are affected by these findings. In the present note, we answer this question in the negative, by means of elementary linear algebra: "geometric" symmetries of toroidal conformal field theories are not doomed to fail. Consequently, and in particular, the symmetry groups involved in symmetry surfing the moduli space of K3 theories do not differ from their lifts.

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On symmetries of N $$ \mathcal{N} $$ = (4, 4) sigma models on T 4

Cited by 21 publications

References 68 publications

Moonshine

Moonshine

K3 string theory, lattices and moonshine

Not doomed to fail

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