A simple approach towards the sign problem using path optimisation

We suggest an approach for simulating theories with a sign problem that relies on optimisation of complex integration contours that are not restricted to lie along Lefschetz thimbles. To that end we consider the toy model of a one-dimensional Bose gas with chemical potential. We identify the main contribution to the sign problem in this case as coming from a nearest neighbour interaction and approximately cancel it by an explicit deformation of the integration contour. We extend the obtained expressions to more general ones, depending on a small set of parameters. We find the optimal values of these parameters on a small lattice and study their range of validity. We also identify precursors for the onset of the sign problem. A fast method of evaluating the Jacobian related to the contour deformation is proposed and its numerical stability is examined. For a particular choice of lattice parameters, we find that our approach increases the lattice size at which the sign problem becomes serious from $L \approx 32$ to $L \approx 700$. The efficient evaluation of the Jacobian ($O(L)$ for a sweep) results in running times that are of the order of a few minutes on a standard laptop.Comment: V1: 25 pages, 8 figures; V2: 28 pages, 8 figures, the methods used for finding the contour parameters are clarified, further discussion added, typos corrected, refs adde

Lattice String Field Theory: The linear dilaton in one dimension

We propose the use of lattice field theory for the study of string field theory at the non-perturbative quantum level. We identify many potential obstacles and examine possible resolutions thereof. We then experiment with our approach in the particularly simple case of a one-dimensional linear dilaton and analyse the results.Comment: V1: 74 pages, 35 figures. V2: 75 pages, 35 figures, refs added, typos corrected, some clarification

Democratic Superstring Field Theory and its Gauge Fixing

This work is my contribution to the proceedings of the conference "SFT2010 - the third international conference on string field theory and related topics" and it reflects my talk there, which described the democratic string field theory and its gauge fixing. The democratic string field theory is the only fully RNS string field theory to date. It lives in the large Hilbert space and includes all picture numbers. Picture changing amounts in this formalism to a gauge transformation. We describe the theory and its properties and show that when partially gauge fixed it can be reduced to the modified theory and to the non-polynomial theory. In the latter case we can even include the Ramond sector in the picture-fixed action. We also show that another partial gauge-fixing leads to a new consistent string field theory at picture number -1.Comment: 10 pages. A contribution to the proceedings of "SFT2010", held at the YITP, Kyoto, Japan, October 18-22, 201

Regularizing Cubic Open Neveu-Schwarz String Field Theory

After introducing non-minimal variables, the midpoint insertion of Y\bar Y in cubic open Neveu-Schwarz string field theory can be replaced with an operator N_\rho depending on a constant parameter \rho. As in cubic open superstring field theory using the pure spinor formalism, the operator N_\rho is invertible and is equal to 1 up to a BRST-trivial quantity. So unlike the linearized equation of motion Y\bar Y QV=0 which requires truncation of the Hilbert space in order to imply QV=0, the linearized equation N_\rho QV=0 directly implies QV=0.Comment: 6 pages harvmac, added footnote and referenc

On the validity of the solution of string field theory

We analyze the realm of validity of the recently found tachyon solution of cubic string field theory. We find that the equation of motion holds in a non trivial way when this solution is contracted with itself. This calculation is needed to conclude the proof of Sen's first conjecture. We also find that the equation of motion holds when the tachyon or gauge solutions are contracted among themselves

Universal regularization for string field theory

We find an analytical regularization for string field theory calculations. This regularization has a simple geometric meaning on the worldsheet, and is therefore universal as level truncation. However, our regularization has the added advantage of being analytical. We illustrate how to apply our regularization to both the discrete and continuous basis for the scalar field and for the bosonized ghost field, both for numerical and analytical calculations. We reexamine the inner products of wedge states, which are known to differ from unity in the oscillator representation in contrast to the expectation from level truncation. These inner products describe also the descent relations of string vertices. The results of applying our regularization strongly suggest that these inner products indeed equal unity. We also revisit Schnabl's algebra and show that the unwanted constant vanishes when using our regularization even in the oscillator representation