# Taylor expansions on Lefschetz thimbles (and not only that)

@article{Renzo2020TaylorEO, title={Taylor expansions on Lefschetz thimbles (and not only that)}, author={Francesco Di Renzo and Simran Singh and K. Zambello}, journal={arXiv: High Energy Physics - Lattice}, year={2020} }

Thimble regularisation is a possible solution to the sign problem, which is evaded by formulating quantum field theories on manifolds where the imaginary part of the action stays constant (Lefschetz thimbles). A major obstacle is due to the fact that one in general needs to collect contributions coming from more than one thimble. Here we explore the idea of performing Taylor expansions on Lefschetz thimbles. We show that in some cases we can compute expansions in regions where only the dominant…

## References

SHOWING 1-10 OF 25 REFERENCES

Thimble regularization at work: from toy models to chiral random matrix theories.

- Physics
- 2015

We apply the Lefschetz thimble formulation of eld theories to a couple of dierent problems. We rst address the solution of a complex 0-dimensional 4 theory. Although very simple, this toy-model makes…

On the Lefschetz thimbles structure of the Thirring model

- Physics
- 2019

The complexification of field variables is an elegant approach to attack the sign problem. In one approach one integrates on Lefschetz thimbles: over them, the imaginary part of the action stays…

Monte Carlo simulations on the Lefschetz thimble: Taming the sign problem

- Physics
- 2013

We present the first practical Monte Carlo calculations of the recently proposed Lefschetz thimble formulation of quantum field theories. Our results provide strong evidence that the numerical sign…

New approach to the sign problem in quantum field theories: High density QCD on a Lefschetz thimble

- Physics
- 2012

It is sometimes speculated that the sign problem that afflicts many quantum field theories might be reduced or even eliminated by choosing an alternative domain of integration within a complexified…

Sign problem and Monte Carlo calculations beyond Lefschetz thimbles

- Physics
- 2015

A bstractWe point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part…

Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density

- Physics
- 2015

A bstractWe investigate Lefschetz thimble structure of the complexified path-integration in the one-dimensional lattice massive Thirring model with finite chemical potential. The lattice model is…

Hybrid Monte Carlo on Lefschetz thimbles — A study of the residual sign problem

- Physics
- 2013

A bstractWe consider a hybrid Monte Carlo algorithm which is applicable to lattice theories defined on Lefschetz thimbles. In the algorithm, any point (field configuration) on a thimble is…

Towards Lefschetz thimbles regularization of heavy-dense QCD

- PhysicsProceedings of The 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)
- 2019

At finite density, lattice simulations are hindered by the well-known sign problem: for finite chemical potentials, the QCD action becomes complex and the Boltzmann weight $e^{-S}$ cannot be…

Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density

- Physics
- 2015

We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase…

One-dimensional QCD in thimble regularization

- Physics
- 2018

QCD in 0+1 dimensions is numerically solved via thimble regularization. In the context of this toy model, a general formalism is presented for SU(N) theories. The sign problem that the theory…