arXiv research

Mathematical formulas for elliptic curve integrals solve anomaly equations.

The present article surveys some mathematical aspects of the BCOV holomorphic anomaly equations introduced by Bershadsky, Cecotti, Ooguri and Vafa. It grew from a series of lectures the authors gave at the Fields Institute in the Thematic Program of Calabi-Yau Varieties in the fall of 2013.

We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries a deformed version of special Kahler geometry which we characterise. The holomo…

We review the polynomial structure of the topological string partition functions as solutions to the holomorphic anomaly equations. We also explain the connection between the ring of propagators defined from special Kähler geometry and the ring of almost-holomorphic modular forms defined on modular curves.

Holomorphic supergravity theory simplifies anomaly cancellation in heterotic moduli.

We show that the property of existence of solution to the Strominger system in dimension six is neither open nor closed under holomorphic deformations of the complex structure. These results are obtained both in the case of positive slope parameter as well as in the case of negative slope parameter in the anomaly cance…

We present an explicit expression of the anomaly formula for the Cappell-Miller holomorphic torsion for Kähler manifolds.

Anomaly flow studied on flat and non-flat nilmanifolds.

Deformed holomorphic Chern-Simons theory yields new instantons.

The paper proves UV finiteness and vanishing anomalies for hybrid topological-holomorphic field theories.

Using Laurent expansions of the Kontsevich-Vishik canonical trace of holomorphic families of classical pseudodifferential operators, we define functionals on the space of Riemannian metrics and investigate their conformal properties, thereby giving a unified description of several conformal invariants and anomalies.

We describe the first order moduli space of heterotic string theory compactifications which preserve $N=1$ supersymmetry in four dimensions, that is, the infinitesimal parameter space of the Strominger system. We establish that if we promote a connection on $TX$ to a field, the moduli space corresponds to deformations …

The paper quantizes hybrid topological-holomorphic field theories on $\mathbb{R}^m imes \mathbb{C}^n$.

The paper defines new modular forms from almost complex manifolds and derives anomaly cancellation formulas.

Paper tackles anomaly detection and RCA in dynamical systems using ICODE Networks.

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 instanton. For heterotic compactifications in dimension six this reduces the choice of …

We initiate the study of a new nonlinear parabolic equation on a Riemann surface. The evolution equation arises as a reduction of the Anomaly flow on a fibration. We obtain a criterion for long-time existence for this flow, and give a range of initial data where a singularity forms in finite time, as well as a range of…

Variant of Seiberg-Witten equations for multiple-spinors connects to stability of holomorphic bundles.

Solves a Monge-Ampère type equation for Nakano positive curvature tensors of holomorphic vector bundles.

Holomorphic solutions vary in Sobolev spaces for Beltrami equations.

New elliptic genera defined for spin manifolds.

Given a Kaehlerian holomorphic fiber bundle whose fiber is a compact homogeneous Kaehler manifold, we describe the perturbed Hermitian-Einstein equations relative to certain holomorphic vector bundles. With respect to special metrics on the holomorphic bundles, there is a dimensional reduction procedure which reduces t…

The Anomaly flow is shown to converge on toric fibrations with the Fu-Yau ansatz, for both positive and negative values of the slope parameter $α'$. This implies both results of Fu and Yau on the existence of solutions for Hull-Strominger systems, which they proved using different methods depending on the sign of $α'$.…

Investigates $J$-equation on holomorphic vector bundles over Kähler manifolds.

Defines new two-variable elliptic genera for manifolds and derives modular forms.

The paper proves conditions for solutions of $J$-equation and deformed Hermitian-Yang-Mills equation on holomorphic submersions.

The holographic duality can be extended to include quantum theories with broken coordinate invariance leading to the appearance of the gravitational anomalies. On the gravity side one adds the gravitational Chern-Simons term to the bulk action which gauge invariance is only up to the boundary terms. We analyze in detai…

Study Hull-Strominger system and Anomaly flow on specific solvmanifolds.

Study connects K3 surfaces to holomorphic metrics, solving complex structure variation.

Study on deforming complex manifolds and Higgs bundles.

The paper introduces new functionals and equations for complex vector bundles.

Paper extends Kobayashi-Hitchin correspondence to non-Kähler manifolds.

We study the four-dimensional effective theory arising from ten-dimensional heterotic supergravity compactified on manifolds with torsion. In particular, given the heterotic superpotential appropriately corrected at $\mathcal{O}(α')$ to account for the Green-Schwarz anomaly cancellation mechanism, we investigate proper…

It is known that given a stable holomorphic pair $(E ,φ)$, where $E$ is a holomorphic vector bundle on a compact Kähler manifold $X$ and $φ$ is a holomorphic section of $E$, the vector bundle $E$ admits a Hermitian metric solving the vortex equation. We generalize this to pairs $(\E ,φ)$, where $\E$ is a reflexive shea…

We introduce $Z$-critical connections for holomorphic vector bundles and prove their existence under stability conditions.

This paper introduces a complex representation for spacelike surfaces in the Lorentz-Minkowski space $L^4$, based in two complex valued functions which can be assumed to be holomorphic or anti-holomorphic. When the immersion is contained in quadrics of $L^4$, the representation then allows us to obtain interesting part…

Study finds conditions for minimum of Donaldson's functional on Higgs bundles with non-holomorphic Higgs fields.

Proves stability of certain vector bundles on Kähler surfaces.

Study calculates curvatures in holomorphic fibrations using degenerate Hermitian forms.

The main new result here is the cancellation of global anomalies in the Type I superstring, with and without D-branes. Our argument here depends on a precise interpretation of the 2-form abelian gauge field using KO-theory; then the anomaly cancellation follows from a geometric form of the full Atiyah-Singer index theo…

We consider the hypothesis that the C-field 4-flux and 7-flux forms in M-theory are in the image of the non-abelian Chern character map from the non-abelian generalized cohomology theory called J-twisted Cohomotopy theory. We prove for M2-brane backgrounds in M-theory on 8-manifolds that such charge quantization of the…

Quantum flag manifold σ-models are integrable and satisfy Ricci flow equations.

Let $M$ be a super Riemann surface with holomorphic distribution $\mathcal{D}$ and $N$ a symplectic manifold with compatible almost complex structure $J$. We call a map $Φ\colon M\to N$ a super $J$-holomorphic curve if its differential maps the almost complex structure on $\mathcal{D}$ to $J$. Such a super $J$-holomorp…

This review discusses solutions to Einstein's equations using twistor theory.

Higher-order geometry modifies Newtonian dynamics and predicts anomalies in spacecraft motion.

Study extended Bogomolny equations on curved space with special boundary conditions.

The article describes canonical metrics on holomorphic fibre bundles.

The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-f…