# Quantum Background Independence In String Theory

@article{Witten1993QuantumBI, title={Quantum Background Independence In String Theory}, author={Edward Witten}, journal={arXiv: High Energy Physics - Theory}, year={1993} }

Not only in physical string theories, but also in some highly simplified situations, background independence has been difficult to understand. It is argued that the ``holomorphic anomaly'' of Bershadsky, Cecotti, Ooguri, and Vafa gives a fundamental explanation of some of the problems. Moreover, their anomaly equation can be interpreted in terms of a rather peculiar quantum version of background independence: in systems afflicted by the anomaly, background independence does not hold order by…

## 243 Citations

### Background Independence in Gauge Theories

- PhysicsAnnales Henri Poincaré
- 2020

Classical field theory is insensitive to the split of the field into a background configuration and a dynamical perturbation. In gauge theories, the situation is complicated by the fact that a…

### Background independence and the open topological string wavefunction

- Mathematics
- 2007

The open topological string partition function in the background of a D-brane on a Calabi-Yau threefold specifies a state in the Hilbert space associated with the quantization of the underlying…

### Holomorphic anomaly and quantum mechanics

- Physics
- 2016

We show that the all-orders WKB periods of one-dimensional quantum mechanical oscillators are governed by the refined holomorphic anomaly equations of topological string theory. We analyze in detail…

### String theory and classical integrable systems

- Physics
- 1994

We discuss diﬀerent formulations and approaches to string theory and 2 d quantum gravity. The generic idea to get a unique description of many diﬀerent string vacua altogether is demonstrated on the…

### Quantum geometry of refined topological strings

- Mathematics, Physics
- 2012

A bstractWe consider branes in refined topological strings. We argue that their wavefunctions satisfy a Schrödinger equation depending on multiple times and prove this in the case where the…

### Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

- Mathematics
- 1994

We develop techniques to compute higher loop string amplitudes for twistedN=2 theories withĉ=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in…

### String theory and classical integrable systems

- Physics
- 1994

We discuss different formulations and approaches to string theory and 2d quantum gravity. The generic idea to get a unique description of many different string vacua altogether is demonstrated on the…

### Topological wave functions and heat equations

- Mathematics
- 2006

It is generally known that the holomorphic anomaly equations in topological string theory reflect the quantum mechanical nature of the topological string partition function. We present two new…

### Comments on BRST quantization of strings

- Physics
- 2005

The BRST quantization of strings is revisited and the derivation of the path integral measure for scattering amplitudes is streamlined. Gauge invariances due to zero modes in the ghost sector are…

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