We revisit 't Hooft anomalies in (1+1)d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)d classical Chern-Simons actions. On the one hand, we prove that certain exotic anomalies can only be realized by non-reflection-positive or non-compact theories; on the other hand, without insisting on reflection-positivity, the exotic anomalies present a caveat to the inflow paradigm. For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1)×SO(2) classical Chern-Simons action with a boundary condition that matches the SO(2) gauge field with the (1+1)d spin connection. Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines. The isotopy anomaly can be canceled by an extrinsic curvature improvement term, but at the cost of creating a periodicity anomaly. We survey the holomorphic bc ghost system which realizes all the exotic consistent anomalies, and end with comments on a subtlety regarding the anomalies of finite subgroups of U(1).

Properties of the subset of polygonal paths in the Hilbert space of paths referring to a<i>d</i>-dimensional quantum-mechanical system are examined. The results are used to discuss various types of polygonal-path approximations appearing in the functional-integration theory. The uniform approximation is applied to extend the definition of the Feynman maps from our previous paper and to prove consistency of this extension. Relations of the extended<i>F</i> _<i>i</i> map to the Wiener integral are given.

The two-dimensional supersymmetric gauged linear sigma model (GLSM) with abelian gauge groups and matter fields has provided many insights into string theory on Calabi--Yau manifolds of a certain type: complete intersections in toric varieties. In this paper, we consider two GLSM constructions with nonabelian gauge groups and charged matter whose infrared CFTs correspond to string propagation on determinantal Calabi-Yau varieties, furnishing another broad class of Calabi-Yau geometries in addition to complete intersections. We show that these two models -- which we refer to as the PAX and the PAXY model -- are dual descriptions of the same low-energy physics. Using GLSM techniques, we determine the quantum Kähler moduli space of these varieties and find no disagreement with existing results in the literature.

Secure Remote Password (SRP) protocol is an augmented Password-based Authenticated Key Exchange (PAKE) protocol based on discrete logarithm problem (DLP) with various attractive security features. Compared with basic PAKE protocols, SRP does not require server to store user’s password and user does not send password to server to authenticate. These features are desirable for secure client-server applications. SRP has gained extensive real-world deployment, including Apple iCloud, 1Password etc. However, with the advent of quantum computer and Shor’s algorithm, classic DLP-based public key cryptography algorithms are no longer secure, including SRP. Motivated by importance of SRP and threat from quantum attacks, we propose a RLWE-based SRP protocol (RLWE-SRP) which inherit advantages from SRP and elegant design from RLWE key exchange. We also present parameter choice and efficient portable C++ implementation of RLWE-SRP. Implementation of our 209-bit secure RLWE-SRP is more than 3x faster than 112-bit secure original SRP protocol, 5.5x faster than 80-bit secure J-PAKE and 14x faster than two 184-bit secure RLWE-based PAKE protocols with more desired properties.

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We investigate the non-BPS realm of 3d N=4 superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d N=4 theories such as mirror symmetry and a protected sector described by topological quantum mechanics (TQM). Supersymmetric localization allows for the exact determination of the conformal and flavor central charges, and the latter can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE data. We examine the implications of the Z_2 mirror action for the SCFT single- and mixed-branch crossing equations for the moment map operators, and apply numerical bootstrap to obtain universal constraints on OPE data for given flavor symmetry groups. A key ingredient in applying the bootstrap analysis is the determination of the mixed-branch superconformal blocks. Among other results, we show that the simplest known self-mirror theory with SU(2)×SU(2) flavor symmetry saturates our bootstrap bounds, which allows us to extract the non-BPS data and examine the self-mirror Z_2 symmetry thereof.

We present the recent work on the noncommutative Fourier transform for subfactors and locally compact quantum groups, a Survey.We give a short introduction to subfactors and locally compact quantum groups and their properties;the Hausdorff-Young inequality and its extremal functions;Young's inequality and its extremal pairs;uncertainty principles and its minimizers;a noncommutative sum set theorem.

We show all the existing TTM implementation schemes have a defect that there exist linearization equations \sum_{i=1,j=1}^{n,m} a_{ij} x_i y_j(x_1,...,x_n) + \sum_{i=1}^n b_i x_i + \sum_{j=1}^m c_j y_j(x_1,...,x_n) + d = 0, which are satisfied by the components y_i(x_1,...,x_n) of the ciphers of the TTM schemes. We further demonstrate that, for the case of the most recent two implementation schemes in two versions of the paper \cite{CM}, where the inventor of TTM used them to refute a claim in \cite{CG}, if we do a linear substitution with the linear equations derived from the linearization equations for a given ciphertext, we can find the plaintext easily by an iteration of the procedure of first search for linear equations by linear combinations and then linear substitution. The computation complexity of the attack on these two schemes is less than 2^{35} over a finite field of size 2^8.

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The Feynman maps introduced first by Truman are examined. The domain considered here consists of the Fresnel-integrable functions in the sense of Albeverio and Hoegh-Krohn; extensions to wider classes of functions will be studied in the following paper. The original definition of the F-maps is slightly modified: we start from the underlying measures on the Hilbert space of paths in order to avoid use of improper integrals. Some new properties of the F-maps are derived. In particular, the dominated convergence theorem is shown to be not valid for the F₁-map (or Feynman integral); this fact is of a certain importance for the classical limit of quantum mechanics.

In this paper, a class of FETI-DP preconditioners is developed for a fast solution of the linear system arising from staggered discontinuous Galerkin discretization of the two-dimensional Stokes equations. The discretization has been recently developed and has the distinctive advantages that it is optimally convergent and has a good local conservation property. In order to efficiently solve the linear system, two kinds of FETI-DP preconditioners, namely, lumped and Dirichlet preconditioners, are considered and analyzed. Scalable bounds C (H/h) and C (1+ log (H/h)) 2 are proved for the lumped and Dirichlet preconditioners, respectively, with the constant C depending on the infsup constant of the discrete spaces but independent of any mesh parameters. Here H/h stands for the number of elements across each subdomain. Numerical results are presented to confirm the theoretical estimates.

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We present a quantum field theoretic description on the t−J model on a square lattice with dilute holes (i.e. near half-filling), based on the compact mutual Chern-Simons gauge theory. We show that, due to the presence of non-perturbative monopole plasma configuration from the antiferromagnetic background, holons (carrying electric charge) are linearly confined and strongly localized even without extrinsic disorder taken into account. Accordingly, the translation symmetry is spontaneously broken at ground state. Such an exotic localization is distinct from Anderson localization and essentially rooted in intrinsic Mott physics of the t−J model. Finally, a finite-temperature phase diagram is proposed. The metal-insulator transition observed in in-plane resistivity measurement is identified to a confinement-deconfinement transition from the perspective of gauge theory. The transition is characterized by the order parameter "Polyakov-line".

We study two-dimensional conformal field theories in the semiclassical limit. In this limit, the four-point function is dominated by intermediate primaries of particular weights along with their descendants, and the crossing equations simplify drastically. For a four-point function receiving sufficiently small contributions from the light primaries, the structure constants involving heavy primaries follow a universal formula. Applying our results to the four-point function of the Z_2 twist field in the symmetric product orbifold, we produce the Hellerman bound and the logarithmically corrected Cardy formula that is valid for h ≥ c/12.

We present a closed form expression for the semiclassical OPE coefficients that are universal for all 2D CFTs with a “weak” light spectrum, by taking the semiclassical limit of the fusion kernel. We match this with a properly regularized and normalized bulk action evaluated on a geometry with three conical defects, analytically continued in the deficit angles beyond the range for which a metric with positive signature exists. The analytically continued geometry has a codimension-one coordinate singularity surrounding the heaviest conical defect. This singularity becomes a horizon after Wick rotating to Lorentzian signature, suggesting a connection between universality and the existence of a horizon.

We study out-of-time ordered four-point functions in two dimensional conformal field theories by suitably analytically continuing the Euclidean correlator. For large central charge theories with a sparse spectrum, chaotic dynamics is revealed in an exponential decay; this is seen directly in the contribution of the vacuum block to the correlation function. However, contributions from individual non-vacuum blocks with large spin and small twist dominate over the vacuum block. We argue, based on holographic intuition, that suitable summations over such intermediate states in the block decomposition of the correlator should be sub-dominant, and attempt to use this criterion to constrain the OPE data with partial success. Along the way we also discuss the relation between the spinning Virasoro blocks and the on-shell worldline action of spinning particles in an asymptotically AdS spacetime.

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We investigate a class of supersymmetric quantum mechanical theories (with two supercharges) having tensor-valued degrees of freedom which are dominated by melon diagrams in the large N limit. One motivation was to examine the interplay between supersymmetry and melonic dominance and potential implications for building toy models of holography. We find a definite tension between supersymmetry (with dynamical bosons) and melonic dominance in this class of systems. More specifically, our theories attain a low energy non-supersymmetric conformal fixed point. The origin of supersymmetry breaking lies in the need to regularize bosonic and fermionic degrees of freedom independently. We investigate various aspects of the low energy spectrum and also comment on related examples with different numbers of supercharges. Along the way we also derive some technical results for SL(2, ℝ) wavefunctions for fermionic excitations.

We study two dimensional N = (2, 2) Landau-Ginzburg models with tensor valued superfields with the aim of constructing large central charge superconformal field theories which are solvable using large N techniques. We demonstrate the viability of such constructions and motivate the study of anisotropic tensor models. Such theories are a novel deformation of tensor models where we break the continuous symmetries while preserving the large N solvability. Specifically, we examine theories with superpotentials involving tensor contractions chosen to pick out melonic diagrams. The anisotropy is introduced by further biasing individual terms by different coefficients, all of the same order, to retain large N scaling. We carry out a detailed analysis of the resulting low energy fixed point and comment on potential applications to holography. Along the way we also examine gauged versions of the models (with partial anisotropy) and find generically that such theories have a non-compact Higgs branch of vacua.

Consider an unstable quantum system that has been found undecayed at an instant s and denote by R(t,s) the rate of its regeneration into an original (undecayed) state at a later instant t+s. It is proved that the reduced evolution is a semigroup, i.e., there is no regeneration at all, provided R(t,s)1/2 can be estimated by a sufficiently regular function that is nondecreasing in s and has zero derivative with respect to t at t=0 for every s. This generalizes the theorem of Misra and Sinha [Helv. Phys. Acta 45, 619 (1972)] in a different direction than in a recent paper by Nishioka [J. Math. Phys. 29, 1860 (1988)].

We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on analyticity and Lorentzian dynamics including aspects of chaos. We derive a formula relating the infinite boost limit, which holographically encodes the “opacity” of bulk scattering, to the action of topological defect lines on local operators. Leveraging the unitary bound on the opacity and the positivity of fusion coefficients, we show that the spectral radii of a large class of topological defect lines are given by their loop expectation values. Factorization also gives a formula relating the local and defect operator algebras and fusion categorical data. We then review factorization in rational conformal field theory from a defect perspective, and examine irrational theories. On the orbifold branch of the c = 1 free boson theory, we find a unified description for the topological defect lines through which the twist fields are factorized; at irrational points, the twist fields factorize through “non-compact” topological defect lines which exhibit continuous defect operator spectra. Along the way, we initiate the development of a formalism to characterize non-compact topological defect lines.

Multivariate Cryptography, as one of the main candidates for establishing post-quantum cryptosystems, provides strong, efficient and well-understood digital signature schemes such as UOV, Rainbow, and Gui. While Gui provides very short signatures, it is, for efficiency reasons, restricted to very small finite fields, which makes it hard to scale it to higher levels of security and leads to large key sizes. In this paper we propose a signature scheme called HMFEv (“Hidden Medium Field Equations”), which can be seen as a multivariate version of HFEv. We obtain our scheme by applying the Vinegar Variation to the MultiHFE encryption scheme of Chen et al. We show both theoretically and by experiments that our new scheme is secure against direct and Rank attacks. In contrast to other schemes of the HFE family such as Gui, HMFEv can be defined over arbitrary base fields and therefore is much more efficient in terms of both performance and memory requirements. Our scheme is therefore a good candidate for the upcoming standardization of post-quantum signature schemes.

In this paper, we consider the numerical approximation of the three-dimensional poroelastic wave equations in the spherical coordinate system. One difficulty in the design of an efficient numerical scheme is that the problem is singular in the center and the polar axes of the computational domain. Nevertheless, we develop a hybrid finite difference/control volume method for solving this problem. Our method is explicit and is second order accurate in both space and time. Numerical results are shown to confirm the convergence rate of our method and the effectiveness to simulate wave propagation in poroelastic media in the spherical coordinate system.

The seek for a new universal formulation for describing various non-equilibrium processes is a central task of modern non-equilibrium thermodynamics. In this paper, a novel steady-state thermodynamic formalism was established for general Markov processes described by the Chapman-Kolmogorov equation. Furthermore, corresponding formalisms of steady-state thermodynamics for master equation and Fokker-Planck equation could be rigorously derived in mathematics. To be concrete, we proved that: 1) in the limit of continuous time, the steady-state thermodynamic formalism for the Chapman-Kolmogorov equation fully agrees with that for the master equation; 2) a similar one-to-one correspondence could be established rigorously between the master equation and Fokker-Planck equation in the limit of large system size; 3) when a Markov process is restrained to one-step jump, the steady-state thermodynamic formalism for the Fokker-Planck equation with discrete state variables also goes to that for master equations, as the discretization step gets smaller and smaller. Our analysis indicated that, with respect to the steady state, general Markov processes admit a unified and self-consistent non-equilibrium thermodynamic formulation, regardless of underlying detailed models.