Little strings on D n orbifolds

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We study the elliptic genera of 6d strings based on their modular properties. They are weak Jacobi forms of weight 0, whose indices are determined from the 2d chiral anomalies. We propose the ansatz for the elliptic genera which reflects the analytic structure of instanton partition functions. Given a finite amount of initial BPS data, we completely determine the elliptic genera of 6d strings in various 6d SCFTs. We also apply our ansatz to study N = (2, 0) and (1, 1) little strings as well as N = (1, 0) heterotic little strings, for which T-duality of little string theories supplies a sufficient number of initial BPS data. The anomaly polynomials of 6d little strings are worked out, which is needed for the elliptic genera bootstrap. In some little string theories, the elliptic genera must have the extra contributions from the Coulomb branch, which correspond to the additional zero modes for the full strings. The modified ansatze for such elliptic genera are also discussed.where (c R − c L ) is the 2d gravitational anomaly. Similarly, the gauge non-invariant action S (2) must match the 2d chiral anomaly under the U (1) gauge transformation, i.e., δ Φ z = 0 and δ A z = d z . Recall that the 2d chiral anomaly ∆ is encoded in the 4-form anomaly polynomial I 4 by the descent formalism, such thatwhere the sum is taken over all background U (1) gauge fields. Dimensionally reducing it on S 1 t ,

Section: Introductionmentioning

confidence: 54%

On elliptic genera of 6d string theories

Kim

Lee

Park

2018

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“…Let us review this in the following where we shall follow in the first half the presentation of [14] (for related work see [5,[29][30][31]). In the framework of little string theories the fiber-base duality reduces to T-duality of two 6d N = (1, 0) theories.…”

Section: Little String Theorymentioning

confidence: 99%

ADE string chains and mirror symmetry

Haghighat

Yan

Yau

2018

6d superconformal field theories (SCFTs) are the SCFTs in the highest possible dimension. They can be geometrically engineered in F-theory by compactifying on noncompact elliptic Calabi-Yau manifolds. In this paper we focus on the class of SCFTs whose base geometry is determined by −2 curves intersecting according to ADE Dynkin diagrams and derive the corresponding mirror Calabi-Yau manifold. The mirror geometry is uniquely determined in terms of the mirror curve which has also an interpretation in terms of the Seiberg-Witten curve of the four-dimensional theory arising from torus compactification. Adding the affine node of the ADE quiver to the base geometry, we connect to recent results on SYZ mirror symmetry for the A case and provide a physical interpretation in terms of little string theory. Our results, however, go beyond this case as our construction naturally covers the D and E cases as well.

“…one M5 brane probing a D 4 singularity) compactified on R 4 × T 2 is captured by the 2d quiver gauge theory shown in Figure 3. It is composed of an E-string node [9] and an O(−4) node [10] combined into a circular −1,−4 chain [31]. k 1 and k 2 denote the winding numbers of two fractional little strings corresponding to the −4 and −1 curves in the Ftheory construction.…”

Section: The Thermodynamic Limitmentioning

confidence: 99%

“…The topological string partition function in this case then boils down to computing the following infinite sum where d Z Sp(k 1 )×O(k 2 ),d denotes the elliptic genus of a string chain composed of k 1 SO(8) instanton strings and k 2 E-strings. We refer to [31] for its precise definition. Notice that care has been taken of the fact that it has discrete gauge moduli labeled by d in the superscript of the elliptic genus.…”

Section: The Thermodynamic Limitmentioning

confidence: 99%

D-type fiber-base duality

Haghighat

Kim

Yan

et al. 2018

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M5 branes probing D-type singularities give rise to 6d (1,0) SCFTs with SO × SO flavor symmetry known as D-type conformal matter theories. Gauging the diagonal SO-flavor symmetry leads to a little string theory with an intrinsic scale which can be engineered in F-theory by compactifying on a doubly-elliptic Calabi-Yau manifold. We derive Seiberg-Witten curves for these little string theories which can be interpreted as mirror curves for the corresponding Calabi-Yau manifolds. Under fiber-base duality these models are mapped to D-type quiver gauge theories and we check that their Seiberg-Witten curves match. By taking decompactification limits, we construct the curves for the related 6d SCFTs and connect to known results in the literature by further taking 5d and 4d limits.