Related papers: Anomaly cancellation formulas and E8 bundles
It has been shown that the Alvarez-Gaum$\mathrm{\acute{e}}$-Witten miraculous anomaly cancellation formula in type IIB superstring theory and its various generalizations can be derived from modularity of certain characteristic forms. In…
In models of oriented closed strings, anomaly cancellations are deeply linked to the {\it modular invariance} of the torus amplitude. If open and/or unoriented strings are allowed, there are no non-trivial modular transformations in the…
We study the instanton partition functions of two well-known superconformal field theories with mass deformations. Two types of anomaly equations, namely, the modular anomaly and holomorphic anomaly, have been discovered in the literature.…
Smooth manifolds of G_2 holonomy, used to compactify M-theory to four dimensions, give only abelian gauge groups without charged matter multiplets. But singular G_2-manifolds can give abelian or nonabelian gauge groups with chiral fermions.…
We generalize the "miraculous cancellation" formulas of Alvarez-Gaum\'e, Witten and Kefeng Liu to a twisted version where an extra complex line bundle is involved. We also apply our result to discuss intrinsic relations between the higher…
We show that six-dimensional backgrounds that are T^2 bundle over a Calabi-Yau two-fold base are consistent smooth solutions of heterotic flux compactifications. We emphasize the importance of the anomaly cancellation condition which can…
We present calculation of the anomaly cancellation in M-theory on orbifolds $S^1/Z_2$ and $T^5/Z_2$ in the upstairs approach. The main requirement that allows one to uniquely define solutions to the modified Bianchi identities in this case…
Anomalous cancellation of fractions is a mathematically inaccurate method where cancelling the common digits of the numerator and denominator correctly reduces it. While it appears to be accidentally successful, the property of anomalous…
Some forms of Lie algebras of types E_6, E_7, and E_8 are constructed using the exterior cube of a rank 9 finitely generated projective module.
I show that anomaly cancellation conditions are sufficient to determine the two most important topological numbers relevant for Calabi-Yau compactification to six dimensions. This reflects the fact that K3 is the only non-trivial CY…
This work provides five explicit constructions of the exceptional Lie algebra $\mathfrak{e}_8$, based on its semisimple subalgebras of maximal rank. Each of these models is graded by an abelian group, namely, $\mathbb{Z}_4$, $\mathbb{Z}_5$,…
We perform a bordism computation to show that the $E_{7(7)}(\mathbb{R})$ U-duality symmetry of 4d $\mathcal N = 8$ supergravity could have an anomaly invisible to perturbative methods; then we show that this anomaly is trivial. We compute…
We use localization techniques to study the non-perturbative properties of an N=2 superconformal gauge theory with gauge group SU(3) and six fundamental flavours. The instanton corrections to the prepotential, the dual periods and the…
We study in detail the pattern of anomaly cancellation in D=6 Type IIB Z_N orientifolds, occurring through a generalized Green-Schwarz mechanism involving several RR antisymmetric tensors and scalars fields. The starting point is a direct…
We show that the heterotic supersymmetry (Killing spinor equations) and the anomaly cancellation imply the heterotic equations of motion in dimensions five, six, seven, eight if and only if the connection on the tangent bundle is an…
We use methods of arithmetic geometry to find solutions to the abelian local anomaly cancellation equations for a four-dimensional gauge theory whose Lie algebra has a single $\mathfrak{u}_1$ summand, assuming that a non-trivial solution…
We calculate the ordinary $C_2$-cohomology, with Burnside ring coefficients, of $BU(2)$, the classifying space for $C_2$-equivariant complex 2-plane bundles, using an extended grading that allows us to capture a more natural set of…
When M-theory is compactified on G_2-holonomy manifolds with conical singularities, charged chiral fermions are present and the low-energy four-dimensional theory is potentially anomalous. We reconsider the issue of anomaly cancellation,…
We display the full anomaly structure of supergravity, including new D-term contributions to the conformal anomaly. This expression has the super-Weyl and chiral U(1)_K transformation properties that are required for implementation of the…
We carefully review the basic examples of anomaly cancellation in M-theory: the 5-brane anomalies and the anomalies on S^1/Z_2. This involves cancellation between quantum anomalies and classical inflow from topological terms. To correctly…