Abstract
We study the discretized worldsheet of Type IIB strings in the Gubser-Klebanov-Polyakov background in a new setup, which eliminates a complex phase previously detected in the fermionic determinant. A sign ambiguity remains, which a study of the fermionic spectrum shows to be related to Yukawa-like terms, including those present in the original Lagrangian before the linearization standard in a lattice QFT approach. Monte Carlo simulations are performed in a large region of the parameter space, where the sign problem starts becoming severe and instabilities appear due to the zero eigenvalues of the fermionic operator. To face these problems, simulations are conducted using the absolute value of a fermionic Pfaffian obtained introducing a small twisted-mass term, acting as an infrared regulator, into the action. The sign of the Pfaffian and the low modes of the quadratic fermionic operator are then taken into account by a reweighting procedure of which we discuss the impact on the measurement of the observables. In this setup we study bosonic and fermionic correlators and observe a divergence in the latter, which we argue — also via a one-loop analysis in lattice perturbation theory — to originate from the U(1)-breaking of our Wilson-like discretization for the fermionic sector.
Highlights
Background [22], and was worked out explicitly in [23]
Monte Carlo simulations are performed in a large region of the parameter space, where the sign problem starts becoming severe and instabilities appear due to the zero eigenvalues of the fermionic operator
The sign of the Pfaffian and the low modes of the quadratic fermionic operator are taken into account by a reweighting procedure of which we discuss the impact on the measurement of the observables
Summary
The Euclidean superstring action in AdS-lightcone gauge-fixing [20, 21] describing quantum fluctuations around the null-cusp background in AdS5 × S5 reads [23]. Generates a non-hermitian term, the last one above, resulting in a complex-valued Pfaffian for the fermionic operator. Though elementary fact that TrΣ±Σ± = 2Tr ΣΣ ± ΣΣgives us some freedom in the choice of the sign in the Lagrangian, since This last equation proves that the complex phase is an artefact of our naive linearization. (2.9) provides two equivalent forms of the same action, one which would lead to a phase problem and one which would not Choosing the latter, i.e. the one involving Σ+, we obtain for the quartic Lagrangian the expression. A “minimal-breaking” solution preserves the SU(4) global symmetry of the Lagrangian and breaks the U(1), and it consists in adding a Wilson-like term in the main diagonal of the fermionic operator. The values of the discretised (scalar) fields are assigned to each lattice site, with periodic boundary conditions for all the fields except for antiperiodic temporal boundary conditions in the case of fermions
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