Related papers: General solution to the U(1) anomaly equations
In this paper, by combining modular forms and characteristic forms, we obtain general anomaly cancellation formulas of any dimension. For $4k+2$ dimensional manifolds, our results include the gravitational anomaly cancellation formulas of…
Many interesting questions about F-theory models, including several concerning the F-theory swampland, involve massless matter charged under U(1) gauge symmetries. It is therefore important to better understand the geometric properties of…
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…
In this paper, we extend the elliptic genus in [10] by the gauge group E_8 and the gauge group E_8*E_8. Then we prove that the generalized elliptic genus are the weak Jacobi forms. Using these elliptic genus, we obtain some SL_2(Z) modular…
A manifestly gauge invariant and regularized renormalization group flow equation is constructed for pure SU(N) gauge theory in the large N limit. In this way we make precise and concrete the notion of a non-perturbative gauge invariant…
A first principles calculation of the quantum corrections to the electric charge of a dyon in an N=2 gauge theory with arbitrary gauge group is presented. These corrections arise from the fermion fields via the mechanism of fermion…
We argue a smallness of gauge couplings in abelian quiver gauge theories, taking the anomaly cancellation condition into account. In theories of our interest there exist chiral fermions leading to chiral gauge anomalies, and an anomaly-free…
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 propose a mechanism which explains the masses of $\eta$ and $\eta'$ mesons without invoking the explicit violation of $U(1)_A$ symmetry by the chiral anomaly. It is shown that the U(1) problem, the problem for which the prediction of…
We report on a detailed calculation of the anomaly coefficients for the odd and even parts of the $Z_2$-graded representation $\theta$ of the Lie algebra Lie$ G$ on the exterior algebra of dimension $2^n$ assuming that $G\subset U(n)$. The…
Extensions of the minimal supersymmetric standard model (MSSM) gauge group abound in the literature. Several of these include an additional $U(1)_X$ gauge group. Chiral fermions' charge assignments under $U(1)_X$ are constrained to cancel…
Starting from the previously constructed effective supergravity theory below the scale of U(1) breaking in orbifold compactifications of the weakly coupled heterotic string, we study the effective theory below the scale of supersymmetry…
We prove the perturbative renormalisability of pure SU(2) Yang-Mills theory in the abelian gauge supplemented with mass terms. Whereas mass terms for the gauge fields charged under the diagonal U(1) allow to preserve the standard form of…
We construct static axially symmetric solutions of SU(2) Einstein-Yang-Mills-dilaton theory. Like their spherically symmetric counterparts, these solutions are nonsingular and asymptotically flat. The solutions are characterized by the…
We sharpen constraints related to hypercharge flux in F-theory GUTs that possess U(1) symmetries and argue that they arise as a consequence of 4-dimensional anomaly cancellation. This gives a physical explanation for all restrictions that…
In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is connected with an autonomous first-order differential equation, solutions of which are used to obtain integral…
A generic feature of string-derived models is the appearance of an anomalous Abelian U(1)_A symmetry which, among other properties, constrains the Yukawa couplings and distinguishes the three families from each other. In this paper, we…
Fermions with magnetic charges can contribute to anomalies. We derive the axial anomaly and gauge anomalies for monopoles and dyons, and find eight new gauge anomaly cancelation conditions in a general theory with both electric and magnetic…
We construct a family of non-invertible topological defects in two-dimensional theories of $n$ Weyl fermions. The construction relies on the existence of $G$-symmetric conformal boundary conditions for $n$ Dirac fermions. Upon unfolding,…
In the 1+1D ultra-local lattice Hamiltonian for staggered fermions with a finite-dimensional Hilbert space, there are two conserved, integer-valued charges that flow in the continuum limit to the vector and axial charges of a massless Dirac…