On the construction of asymmetric orbifold models

Aoki, Kenichiro; D’Hoker, Eric; Phong, Duong H.

doi:10.1016/j.nuclphysb.2004.06.038

Cited by 35 publications

(81 citation statements)

References 53 publications

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“…We have had some initial discussions about this idea with D. Gaiotto and N. Seiberg and we hope to develop this approach further in the future. Moreover, one can interpret many aspects of our discussion in the language of defects [37] and it might be fruitful to use the 11 The µ,μ are arbitrary real numbers in general. The branch of the logarithm is defined by q µ := exp[2πiµτ ].…”

Section: Future Directionsmentioning

confidence: 99%

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An uplifting discussion of T-duality

Harvey

Moore

2018

J. High Energ. Phys.

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It is well known that string theory has a T-duality symmetry relating circle compactifications of large and small radius. This symmetry plays a foundational role in string theory. We note here that while T-duality is order two acting on the moduli space of compactifications, it is order four in its action on the conformal field theory state space. More generally, involutions in the Weyl group W (G) which act at points of enhanced G symmetry have canonical lifts to order four elements of G, a phenomenon first investigated by J. Tits in the mathematical literature on Lie groups and generalized here to conformal field theory. This simple fact has a number of interesting consequences. One consequence is a reevaluation of a mod two condition appearing in asymmetric orbifold constructions. We also briefly discuss the implications for the idea that T-duality and its generalizations should be thought of as discrete gauge symmetries in spacetime. May 22, 20181 We are actually being somewhat sloppy here from a mathematical viewpoint. (Most physicists will want to skip this footnote.) The "Narain moduli space" is an orbifold, and is more properly regarded as a global stack where the automorphism group of objects is always a finite group. However, it is not really the moduli stack of toroidal conformal field theories. In the latter stack, the automorphism group of an object will include continuous groups at, for example, the points of enhanced A-D-E symmetry, while in the Narain moduli stack the automorphism group of the A-D-E points is a finite group F (Γ(g)) discussed at length below. The moduli stack of conformal field theories maps to the Narain moduli space.

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Section: Future Directionsmentioning

confidence: 99%

“…In that case one sums over isomorphism classes of J-bundles with connection 8. The term "modular covariance" was used in a slightly different way in[11] where the term is used for the same identity but with the phase e iφ(γ) put to one.…”

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confidence: 99%

An uplifting discussion of T-duality

Harvey

Moore

2018

J. High Energ. Phys.

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“…where the R-flux cannot be eliminated by any T-duality) as orbifolds with asymmetric twists and shifts. Finding well-defined asymmetric actions is, however, a non-trivial task, due to the difficulty in satisfying the constraints of (multi-loop) modular invariance [10,11,90] (see also [91,92] for examples of asymmetric constructions). As we have seen in the previous section, the presence of Q-flux was related to the asymmetry in the T d "fiber".…”

Section: R-backgrounds From Orbifolds With Asymmetric Twists and Shiftsmentioning

confidence: 99%

Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s

Condeescu

Florakis

Kounnas

et al. 2013

J. High Energ. Phys.

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Abstract:We investigate the orbifold limits of string theory compactifications with geometric and non-geometric fluxes. Exploiting the connection between internal fluxes and structure constants of the gaugings in the reduced supergravity theory, we can identify the types of fluxes arising in certain classes of freely-acting symmetric and asymmetric orbifolds. We give a general procedure for deriving the gauge algebra of the effective gauged supergravity using the exact CFT description at the orbifold point. We find that the asymmetry is, in general, related to the presence of non-geometric Q-and R-fluxes. The action of T-duality is studied explicitly on various orbifold models and the resulting transformation of the fluxes is derived. Several explicit examples are provided, including compactifications with geometric fluxes, Q-backgrounds (T-folds) and R-backgrounds. In particular, we present an asymmetric Z 4 × Z 2 orbifold in which all geometric and nongeometric fluxes ω, H, Q, R are turned on simultaneously. We also derive the corresponding flux backgrounds, which are not in general T-dual to geometric ones, and may even simultaneously depend non-trivially on both the coordinates and their winding T-duals.

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“…The determination of K is a difficult issue, and we shall discuss it further in a forthcoming publication [24]. In this paper, we shall examine only the chiral models, that is, only the issue of vanishing of the chiral blocks dµ…”

Section: Aε Cεmentioning

confidence: 99%

Two-loop superstrings on orbifold compactifications

2004

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The two-loop chiral measure for superstring theories compactified on Z 2 reflection orbifolds is constructed from first principles for even spin structures. This is achieved by a careful implementation of the chiral splitting procedure in the twisted sectors and the identification of a subtle worldsheet supersymmetric and supermoduli dependent shift in the Prym period. The construction is generalized to compactifications which involve more general NS backgrounds preserving worldsheet supersymmetry. The measures are unambiguous and independent of the gauge slice.Two applications are presented, both to superstring compactifications where 4 dimensions are Z 2 -twisted and where the GSO projection involves a chiral summation over spin structures. The first is an orbifold by a single Z 2 -twist; here, orbifolding reproduces a supersymmetric theory and it is shown that its cosmological constant indeed vanishes. The second model is of the type proposed by Kachru-KumarSilverstein and additionally imposes a Z 2 -twist by the parity of worldsheet fermion number; it is shown here that the corresponding cosmological constant does not vanish pointwise on moduli space.

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On the construction of asymmetric orbifold models

Cited by 35 publications

References 53 publications

An uplifting discussion of T-duality

An uplifting discussion of T-duality

Gauged supergravities and non-geometric Q/R-fluxes from asymmetric orbifold CFT’s

Two-loop superstrings on orbifold compactifications

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