# Twisted de Rham cohomology, homological definition of the integral and “Physics over a ring”

@article{Schwarz2008TwistedDR, title={Twisted de Rham cohomology, homological definition of the integral and “Physics over a ring”}, author={Albert S. Schwarz and Ilya L. Shapiro}, journal={Nuclear Physics}, year={2008}, volume={809}, pages={547-560} }

## 28 Citations

### Homological Perturbation Theory for Nonperturbative Integrals

- Mathematics
- 2012

We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of…

### Homological Perturbation Theory for Nonperturbative Integrals

- MathematicsLetters in Mathematical Physics
- 2015

We use the homological perturbation lemma to produce explicit formulas computing the class in the twisted de Rham complex represented by an arbitrary polynomial. This is a non-asymptotic version of…

### Intersection Numbers in Quantum Mechanics and Field Theory

- Mathematics
- 2022

By elaborating on the recent progress made in the area of Feynman integrals, we apply the intersection theory for twisted de Rham cohomologies to simple integrals involving orthogonal polynomials,…

### Real Blow-Up Spaces and Moderate de Rham Complexes

- Mathematics
- 2013

The purpose of this chapter is to give a global construction of the real blow-up space of a complex manifold along a family of divisors. On this space is defined the sheaf of holomorphic functions…

### The Riemann–Hilbert Correspondence for Good Meromorphic Connections (Case of a Smooth Divisor)

- Mathematics
- 2013

This chapter is similar to Chap. 5, but we add holomorphic parameters. Moreover, we assume that no jump occurs in the exponential factors, with respect to the parameters. This is the meaning of the…

### Twisted Differential String and Fivebrane Structures

- Mathematics
- 2009

In the background effective field theory of heterotic string theory, the Green-Schwarz anomaly cancellation mechanism plays a key role. Here we reinterpret it and its magnetic dual version in terms…

### Introduction to Arithmetic Mirror Symmetry

- Mathematics
- 2015

We describe how to find period integrals and Picard-Fuchs differential equations for certain one-parameter families of Calabi-Yau manifolds. These families can be seen as varieties over a finite…

### $p$-adic Berglund-H\"ubsch Duality

- Mathematics
- 2014

Berglund-H\"ubsch duality is an example of mirror symmetry between orbifold Landau-Ginzburg models. In this paper we study a D-module-theoretic variant of Borisov's proof of Berglund-H\"ubsch…

### Applications of the Riemann–Hilbert Correspondence to Holonomic Distributions

- Mathematics
- 2013

To any holonomic \(\mathcal{D}\)-module on a Riemann surface X is associated its Hermitian dual, according to M. Kashiwara. We give a proof that the Hermitian dual is also holonomic. As an…

### Introduction to Arithmetic Mirror Symmetry

- Mathematics
- 2014

We describe how to find period integrals and Picard-Fuchs dif ferential equations for certain one-parameter families of Calabi-Ya u manifolds. These families can be seen as varieties over a finite…

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- Mathematics
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- Mathematics
- 2006

The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are…

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