Publications

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Perturbative unitarity and the wavefunction of the Universe

Soner Albayrak, Paolo Benincasa, Carlos Duaso Pueyo

SciPost Phys. 16, 157 (2024) · published 20 June 2024 | · pdf

Unitarity of time evolution is one of the basic principles constraining physical processes. Its consequences in the perturbative Bunch-Davies wavefunction in cosmology have been formulated in terms of the cosmological optical theorem. In this paper, we re-analyse perturbative unitarity for the Bunch-Davies wavefunction, focusing on: $i)$ the role of the $i\epsilon$-prescription and its compatibility with the requirement of unitarity; $ii)$ the origin of the different ``cutting rules''; $iii)$ the emergence of the flat-space optical theorem from the cosmological one. We take the combinatorial point of view of the cosmological polytopes, which provide a first-principle description for a large class of scalar graphs contributing to the wavefunctional. The requirement of the positivity of the geometry together with the preservation of its orientation determine the $i\epsilon$-prescription. In kinematic space it translates into giving a small negative imaginary part to all the energies, making the wavefunction coefficients well-defined for any value of their real part along the real axis. Unitarity is instead encoded into a non-convex part of the cosmological polytope, which we name \textit{optical polytope}. The cosmological optical theorem emerges as the equivalence between a specific polytope subdivision of the optical polytope and its triangulations, each of which provides different cutting rules. The flat-space optical theorem instead emerges from the non-convexity of the optical polytope. On the more mathematical side, we provide two definitions of this non-convex geometry, none of them based on the idea of the non-convex geometry as a union of convex ones.
Symmetry energy in holographic QCD

Lorenzo Bartolini, Sven Bjarke Gudnason

SciPost Phys. 16, 156 (2024) · published 19 June 2024 | · pdf

We study the symmetry energy (SE), an important quantity in nuclear physics, in the Witten-Sakai-Sugimoto model and in a much simpler hard-wall model of holographic QCD. The SE is the energy contribution to the nucleus due to having an unequal number of neutrons and protons. Using a homogeneous Ansatz representing smeared instantons and quantizing their isospin, we extract the SE and the proton fraction assuming charge neutrality and beta-equilibrium, using quantization of the isospin zeromode. We also show the equivalence between our method adapted from solitons and the usual way of the isospin controlled by a chemical potential at the holographic boundary. We find that the SE can be well described in the WSS model if we allow for a larger 't Hooft coupling and lower Kaluza-Klein scale than is normally used in phenomenological fits.
Large N instantons from topological strings

Marcos Mariño, Ramon Miravitllas

SciPost Phys. 16, 155 (2024) · published 19 June 2024 | · pdf

The $1/N$ expansion of matrix models is asymptotic, and it requires non-perturbative corrections due to large $N$ instantons. Explicit expressions for large $N$ instanton amplitudes are known in the case of Hermitian matrix models with one cut, but not in the multi-cut case. We show that the recent exact results on topological string instanton amplitudes provide the non-perturbative contributions of large $N$ instantons in generic multi-cut, Hermitian matrix models. We present a detailed test in the case of the cubic matrix model by considering the asymptotics of its $1/N$ expansion, which we obtain at relatively high genus for a generic two-cut background. These results can be extended to certain non-conventional matrix models which admit a topological string theory description. As an application, we determine the large $N$ instanton corrections for the free energy of ABJM theory on the three-sphere, which correspond to D-brane instanton corrections in superstring theory. We also illustrate the applications of topological string instantons in a more mathematical setting by considering orbifold Gromov-Witten invariants. By focusing on the example of ${\mathbb C}^3/{\mathbb Z}_3$, we show that they grow doubly-factorially with the genus and we obtain and test explicit asymptotic formulae for them.
Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space

Nathan Seiberg, Sahand Seifnashri, Shu-Heng Shao

SciPost Phys. 16, 154 (2024) · published 17 June 2024 | · pdf

We discuss the exact non-invertible Kramers-Wannier symmetry of 1+1d lattice models on a tensor product Hilbert space of qubits. This symmetry is associated with a topological defect and a conserved operator, and the latter can be presented as a matrix product operator. Importantly, unlike its continuum counterpart, the symmetry algebra involves lattice translations. Consequently, it is not described by a fusion category. In the presence of this defect, the symmetry algebra involving parity/time-reversal is realized projectively, which is reminiscent of an anomaly. Different Hamiltonians with the same lattice non-invertible symmetry can flow in their continuum limits to infinitely many different fusion categories (with different Frobenius-Schur indicators), including, as a special case, the Ising CFT. The non-invertible symmetry leads to a constraint similar to that of Lieb-Schultz-Mattis, implying that the system cannot have a unique gapped ground state. It is either in a gapless phase or in a gapped phase with three (or a multiple of three) ground states, associated with the spontaneous breaking of the lattice non-invertible symmetry.

1 citation
Carroll fermions

Eric A. Bergshoeff, Andrea Campoleoni, Andrea Fontanella, Lea Mele, Jan Rosseel

SciPost Phys. 16, 153 (2024) · published 14 June 2024 | · pdf

Using carefully chosen projections, we consider different Carroll limits of relativistic Dirac fermions in any spacetime dimensions. These limits define Carroll fermions of two types: electric and magnetic. The latter type transforms as a reducible but indecomposable representation of the Carroll group. We also build action principles for all Carroll fermions we introduce; in particular, in even dimensions we provide an action principle for a minimal magnetic Carroll fermion, having the same number of components as a Dirac spinor. We then explore the coupling of these fermions to magnetic Carroll gravity in both its first-order and second-order formulations.
Geometric surprises in the Python's lunch conjecture

Gurbir Arora, Matthew Headrick, Albion Lawrence, Martin Sasieta, Connor Wolfe

SciPost Phys. 16, 152 (2024) · published 12 June 2024 | · pdf

A bulge surface, on a time reflection-symmetric Cauchy slice of a holographic spacetime, is a non-minimal extremal surface that occurs between two locally minimal surfaces homologous to a given boundary region. According to the python's lunch conjecture of Brown et al., the bulge's area controls the complexity of bulk reconstruction, in the sense of the amount of post-selection that needs to be overcome for the reconstruction of the entanglement wedge beyond the outermost extremal surface. We study the geometry of bulges in a variety of classical spacetimes, and discover a number of surprising features that distinguish them from more familiar extremal surfaces such as Ryu-Takayanagi surfaces: they spontaneously break spatial isometries, both continuous and discrete; they are sensitive to the choice of boundary infrared regulator; they can self-intersect; and they probe entanglement shadows, orbifold singularities, and compact spaces such as the sphere in AdS$_p× S^q$. These features imply, according to the python's lunch conjecture, novel qualitative differences between complexity and entanglement in the holographic context. We also find, surprisingly, that extended black brane interiors have a non-extensive complexity; similarly, for multi-boundary wormhole states, the complexity pleateaus after a certain number of boundaries have been included.
Free energy and metastable states in the square-lattice $J_1$-$J_2$ Ising model

Veniamin A. Abalmasov

SciPost Phys. 16, 151 (2024) · published 6 June 2024 | · pdf

Free energy as a function of polarization is calculated for the square-lattice $J_1$-$J_2$ Ising model for $J_2 < |J_1|/2$ using the random local field approximation (RLFA) and Monte Carlo (MC) simulations. Within RLFA, it reveals a metastable state with zero polarization in the ordered phase. In addition, the Landau free energy calculated within RLFA indicates a geometric slab-droplet phase transition at low temperature, which cannot be predicted by the mean field approximation. In turn, restricted free energy calculations for finite-size samples, exact and using MC simulations, reveal metastable states with a wide range of polarization values, but with only two domains. Taking into account the dependence of the restricted free energy on the nearest-neighbor correlations allows us to identify several more metastable states. The calculations also reveal additional slab-droplet transitions at $J_2 > |J_1|/4$. These findings enrich our knowledge of the $J_1$-$J_2$ Ising model and the RLFA as a useful theoretical tool to study phase transitions in spin systems.
On $\varepsilon$-factorised bases and pure Feynman integrals

Hjalte Frellesvig, Stefan Weinzierl

SciPost Phys. 16, 150 (2024) · published 6 June 2024 | · pdf

We investigate $\varepsilon$-factorised differential equations, uniform transcendental weight and purity for Feynman integrals. We are in particular interested in Feynman integrals beyond the ones which evaluate to multiple polylogarithms. We show that a $\varepsilon$-factorised differential equation does not necessarily lead to Feynman integrals of uniform transcendental weight. We also point out that a proposed definition of purity works locally, but not globally.
Scaling limit of the staggered six-vertex model with $U_q\big(\mathfrak{sl}(2)\big)$ invariant boundary conditions

Holger Frahm, Sascha Gehrmann, Gleb Andreevich Kotousov

SciPost Phys. 16, 149 (2024) · published 5 June 2024 | · pdf

We study the scaling limit of a statistical system, which is a special case of the integrable inhomogeneous six-vertex model. It possesses $U_q\big(\mathfrak{sl}(2)\big)$ invariance due to the choice of open boundary conditions imposed. An interesting feature of the lattice theory is that the spectrum of scaling dimensions contains a continuous component. By applying the ODE/IQFT correspondence and the method of the Baxter $Q$ operator the corresponding density of states is obtained. In addition, the partition function appearing in the scaling limit of the lattice model is computed, which may be of interest for the study of nonrational CFTs in the presence of boundaries. As a side result of the research, a simple formula for the matrix elements of the $Q$ operator for the general, integrable, inhomogeneous six-vertex model was discovered, that has not yet appeared in the literature. It is valid for a certain one parameter family of diagonal open boundary conditions in the sector with the $z$-projection of the total spin operator being equal to zero.
The two critical temperatures conundrum in La$_{1.83}$Sr$_{0.17}$CuO$_4$

Abhisek Samanta, Itay Mangel, Amit Keren, Daniel P. Arovas, Assa Auerbach

SciPost Phys. 16, 148 (2024) · published 5 June 2024 | · pdf

The in-plane and out-of-plane superconducting stiffness of ${\rm La}^{\vphantom{\dagger}}_{1.83}{\rm Sr}^{\vphantom{\dagger}}_{0.17}{\rm CuO}^{\vphantom{\dagger}}_4$ rings appear to vanish at different transition temperatures, which contradicts thermodynamical expectation. In addition, we observe a surprisingly strong dependence of the out-of-plane stiffness transition on sample width. With evidence from Monte Carlo simulations, this effect is explained by very small ratio $\alpha$ of inter-plane over intra-plane Josephson couplings. For three dimensional rings of millimeter dimensions, a crossover from layered three dimensional to quasi one dimensional behavior occurs at temperatures near the thermodynamic transition temperature ${T_{\rm c}}$, and the out-of-plane stiffness appears to vanish below ${T_{\rm c}}$ by a temperature shift of order $\alpha L_a/{\xi^{\parallel}}$, where $L_a/{\xi^{\parallel}}$ is the sample's width over coherence length. Including the effects of layer-correlated disorder, the measured temperature shifts can be fit by a value of $\alpha=4.1× 10^{-5}$, near ${T_{\rm c}}$, which is significantly lower than its previously measured value near zero temperature.

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Publications

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