From 6D superconformal field theories to dynamic gauged linear sigma models

We consider the 6d (2, 0) theory on a fibration by genus g curves, and dimensionally reduce along the fiber to 4d theories with duality defects. This generalizes class S theories, for which the fibration is trivial. The non-trivial fibration in the present setup implies that the gauge couplings of the 4d theory, which are encoded in the complex structures of the curve, vary and can undergo S-duality transformations. These monodromies occur around 2d loci in spacetime, the duality defects, above which the fiber is singular. The key role that the fibration plays here motivates refering to this setup as theories of class F. In the simplest instance this gives rise to 4d N = 4 Super-Yang-Mills with space-time dependent coupling that undergoes SL(2, Z) monodromies. We determine the anomaly polynomial for these theories by pushing forward the anomaly polynomial of the 6d (2, 0) theory along the fiber. This gives rise to corrections to the anomaly polynomials of 4d N = 4 SYM and theories of class S. For the torus case, this analysis is complemented with a field theoretic derivation of a U (1) anomaly in 4d N = 4 SYM. The corresponding anomaly polynomial is tested against known expressions of anomalies for wrapped D3-branes with varying coupling, which are known field theoretically and from holography. Extensions of the construction to 4d N = 0 and 1, and 2d theories with varying coupling, are also discussed.

“…When integrating we find This matches the anomaly polynomial given in [68] for compactifications of 6d SCFTs on, not necessarily elliptic, Kähler four-manifolds.…”

Section: D Conformal Matter Theories and Class Fsupporting

confidence: 82%

Theories of class F and anomalies

Lawrie

Martelli

Schäfer‐Nameki

2018

“…Another immediate question for future research concerns the relation between the cohomological identities described in this work and the structure of anomalies in 2-dimensional N = (0, 2) supersymmetric F-theory compactifications on Calabi-Yau 5-folds [50][51][52][53]. A notable difference from compactifications to four and six dimensions is the appearance of chiral charged zero modes at the intersection of 7-branes and D3-branes wrapping curves on the base of the fibration.…”

Section: Jhep11(2017)100mentioning

confidence: 94%

Algebraic cycles and local anomalies in F-theory

Bies

Mayrhofer²,

Weigand

2017

We introduce a set of identities in the cohomology ring of elliptic fibrations which are equivalent to the cancellation of gauge and mixed gauge-gravitational anomalies in F-theory compactifications to four and six dimensions. The identities consist in (co)homological relations between complex codimension-two cycles. The same set of relations, once evaluated on elliptic Calabi-Yau three-folds and four-folds, is shown to universally govern the structure of anomalies and their Green-Schwarz cancellation in sixand four-dimensional F-theory vacua, respectively. We furthermore conjecture that these relations hold not only within the cohomology ring, but even at the level of the Chow ring, i.e. as relations among codimension-two cycles modulo rational equivalence. We verify this conjecture in non-trivial examples with Abelian and non-Abelian gauge groups factors. Apart from governing the structure of local anomalies, the identities in the Chow ring relate different types of gauge backgrounds on elliptically fibred Calabi-Yau four-folds.

“…Constructions of 2d (0, 2) theories in other corners of string theory and F-theory have been presented in [14][15][16][17][18][19][20]. The corresponding Green-Schwarz mechanism for anomaly cancellation was studied in [21].…”

Section: Jhep05(2018)082mentioning

confidence: 99%

3d printing of 2d $$ \mathcal{N}=\left(0,2\right) $$ gauge theories

Franco

Hasan

2018

We introduce 3d printing, a new algorithm for generating 2d N = (0, 2) gauge theories on D1-branes probing singular toric Calabi-Yau 4-folds using 4d N = 1 gauge theories on D3-branes probing toric Calabi-Yau 3-folds as starting points. Equivalently, this method produces brane brick models starting from brane tilings. 3d printing represents a significant improvement with respect to previously available tools, allowing a straightforward determination of gauge theories for geometries that until now could only be tackled using partial resolution. We investigate the interplay between triality, an IR equivalence between different 2d N = (0, 2) gauge theories, and the freedom in 3d printing given an underlying Calabi-Yau 4-fold. Finally, we present the first discussion of the consistency and reduction of brane brick models.