Explicit Realization Research Articles

Galois Conjugated Tensor Fusion Categories and Nonunitary Conformal Field Theory.

We provide a generalization of the matrix product operator formalism for string-net projected entangled pair states (PEPS) to include nonunitary solutions of the pentagon equation. These states provide the explicit lattice realization of the Galois conjugated counterparts of (2+1)-dimensional topological quantum field theories, based on tensor fusion categories. Although the parent Hamiltonians of these renormalization group fixed point states are gapless, these states can still be the topological ground states of a gapped non-Hermitian Hamiltonian. We show by example that the topological sectors of the Yang-Lee theory (the nonunitary counterpart of the Fibonacci fusion category) can be constructed, even in the absence of closure under Hermitian conjugation of the basis elements of the Ocneanu tube algebra. The topological sector construction is demonstrated by applying the concept of strange correlators to the Yang-Lee model, giving rise to a nonunitary version of the classical hard hexagon model in the Yang-Lee universality class and obtaining all generalized twisted boundary conditions on a finite cylinder of the Yang-Lee edge singularity. Finally, we construct the PEPS transfer matrix and show that taking the Hermitian conjugate changes the topological phase for these nonunitary string-net models.

Twisted toroidal Lie algebras and Moody-Rao-Yokonuma presentation

Let $\fg$ be an affine Kac-Moody algebra, and $\mu$ a diagram automorphism of $\fg$. In this paper, we give an explicit realization for the universal central extension $\wh\fg[\mu]$ of the twisted loop algebra of $\fg$ related to $\mu$, which provides a Moody-Rao-Yokonuma presentation for the algebra $\wh\fg[\mu]$ when $\mu$ is non-transitive, and the presentation is indeed related to the quantization of toroidal Lie algebras.

Spacetime Structure near Generic Horizons and Soft Hair.

We explore the spacetime structure near nonextremal horizons in any spacetime dimension greater than two and discover a wealth of novel results: (i)Different boundary conditions are specified by a functional of the dynamical variables, describing inequivalent interactions at the horizon with a thermal bath. (ii)The near horizon algebra of a set of boundary conditions, labeled by a parameter s, is given by the semidirect sum of diffeomorphisms at the horizon with "spin-s supertranslations." For s=1 we obtain the first explicit near horizon realization of the Bondi-Metzner-Sachs algebra. (iii)For another choice, we find a nonlinear extension of the Heisenberg algebra, generalizing recent results in three spacetime dimensions. This algebra allows us to recover the aforementioned (linear) ones as composites. (iv)These examples allow us to equip not only black holes, but also cosmological horizons with soft hair. We also discuss implications of soft hair for black hole thermodynamics and entropy.

Logarithmic loop corrections, moduli stabilisation and de Sitter vacua in string theory

We study string loop corrections to the gravity kinetic terms in type IIB com- pactifications on Calabi-Yau threefolds or their orbifold limits, in the presence of D7-branes and orientifold planes. We show that they exhibit in general a logarithmic behaviour in the large volume limit transverse to the D7-branes, induced by a localised four-dimensional Einstein-Hilbert action that appears at a lower order in the closed string sector, found in the past. Here, we compute the coefficient of the logarithmic corrections and use them to provide an explicit realisation of a mechanism for Kähler moduli stabilisation that we have proposed recently, which does not rely on non-perturbative effects and lead to de Sit- ter vacua. Our result avoids no-go theorems of perturbative stabilisation due to runaway potentials, in a way similar to the Coleman-Weinberg mechanism, and provides a counter example to one of the swampland conjectures concerning de Sitter vacua in quantum grav- ity, once string loop effects are taken into account; it thus paves the way for embedding the Standard Model of particle physics and cosmology in string theory.

Gluing gravitational blocks for AdS black holes

We provide a unifying entropy functional and an extremization principle for black holes and black strings in AdS4 × S7 and AdS5 × S5 with arbitrary rotation and generic electric and magnetic charges. This is done by gluing gravitational blocks, basic building blocks that are directly inspired by the holomorphic blocks appearing in the factorization of supersymmetric partition functions in three and four dimensions. We also provide an explicit realization of the attractor mechanism by identifying the values of the scalar fields at the horizon with the critical points of the entropy functional. We give examples based on dyonic rotating black holes with a twist in AdS4 × S7, rotating black strings in AdS5 × S5, dyonic Kerr-Newman black holes in AdS4 × S7 and Kerr-Newman black holes in AdS5 × S5. In particular, our entropy functional extends existing results by adding rotation to the twisted black holes in AdS4 and by adding flavor magnetic charges for the Kerr-Newman black holes in AdS4. We also discuss generalizations to higher-dimensional black objects.

General fractional calculus and Prabhakar’s theory

General fractional calculus offers an elegant and self-consistent path toward the generalization of fractional calculus to an enhanced class of kernels. Prabhakar’s theory can be thought of, to some extent, as an explicit realization of this scheme achieved by merging the Prabhakar (or, three-parameter Mittag-Leffler) function with the general wisdom of the standard (Riemann-Liouville and Caputo) formulation of fractional calculus. Here I discuss some implications that emerge when attempting to frame Prabhakar’s theory within the program of general fractional calculus.

Emergence and full 3D-imaging of nodal boundary Seifert surfaces in 4D topological matter

The topological classification of nodal links and knot has enamored physicists and mathematicians alike, both for its mathematical elegance and implications on optical and transport phenomena. Central to this pursuit is the Seifert surface bounding the link/knot, which has for long remained a mathematical abstraction. Here we propose an experimentally realistic setup where Seifert surfaces emerge as boundary states of 4D topological systems constructed by stacking 3D nodal line systems along a 4th quasimomentum. We provide an explicit realization with 4D circuit lattices, which are freed from symmetry constraints and are readily tunable due to the dimension and distance agnostic nature of circuit connections. Importantly, their Seifert surfaces can be imaged in 3D via their pronounced impedance peaks, and are directly related to knot invariants like the Alexander polynomial and knot Signature. This work thus unleashes the great potential of Seifert surfaces as sophisticated yet accessible tools in exotic bandstructure studies.

The Higher Rank q-Deformed Bannai-Ito and Askey-Wilson Algebra

The $q$-deformed Bannai-Ito algebra was recently constructed in the threefold tensor product of the quantum superalgebra $\mathfrak{osp}_q(1\vert 2)$. It turned out to be isomorphic to the Askey-Wilson algebra. In the present paper these results will be extended to higher rank. The rank $n-2$ $q$-Bannai-Ito algebra $\mathcal{A}_n^q$, which by the established isomorphism also yields a higher rank version of the Askey-Wilson algebra, is constructed in the $n$-fold tensor product of $\mathfrak{osp}_q(1\vert 2)$. An explicit realization in terms of $q$-shift operators and reflections is proposed, which will be called the $\mathbb{Z}_2^n$ $q$-Dirac-Dunkl model. The algebra $\mathcal{A}_n^q$ is shown to arise as the symmetry algebra of the constructed $\mathbb{Z}_2^n$ $q$-Dirac-Dunkl operator and to act irreducibly on modules of its polynomial null-solutions. An explicit basis for these modules is obtained using a $q$-deformed $\mathbf{CK}$-extension and Fischer decomposition.

SUSY $N$-supergroups and their real forms

We study SUSY N-supergroups, N = 1, 2, their classification and explicit realization, together with their real forms. In the end, we give the supergroup of SUSY preserving automorphisms of C1|1 and we identify it with a subsupergroup of the SUSY preserving automorphisms of P.

’t Hooft Anomalies of Discrete Gauge Theories and Non-abelian Group Cohomology

We study discrete symmetries of Dijkgraaf-Witten theories and their gauging in the framework of (extended) functorial quantum field theory. Non-abelian group cohomology is used to describe discrete symmetries and we derive concrete conditions for such a symmetry to admit 't Hooft anomalies in terms of the Lyndon-Hochschild-Serre spectral sequence. We give an explicit realization of a discrete gauge theory with 't Hooft anomaly as a state on the boundary of a higher-dimensional Dijkgraaf-Witten theory. This allows us to calculate the 2-cocycle twisting the projective representation of physical symmetries via transgression. We present a general discussion of the bulk-boundary correspondence at the level of partition functions and state spaces, which we make explicit for discrete gauge theories.

Quantum algebra from generalized q-Hermite polynomials

In this paper, we discuss new results related to the generalized discrete q-Hermite II polynomials h˜n,α(x;q), introduced by Mezlini et al. in 2014. Our aim is to give a continuous orthogonality relation, a q-integral representation and an evaluation at unity of the Poisson kernel, for these polynomials. Furthermore, we introduce q-Schrödinger operators and we give the raising and lowering operator algebra corresponding to these polynomials. Our results generate a new explicit realization of the quantum algebra suq(1,1), using the generators associated with a q-deformed generalized para-Bose oscillator.

A Discrete Realization of the Higher Rank Racah Algebra

In previous work, a higher rank generalization R(n) of the Racah algebra was defined abstractly. The special case of rank one encodes the bispectrality of the univariate Racah polynomials and is known to admit an explicit realization in terms of the operators associated with these polynomials. Starting from the Dunkl model for which we have an action by R(n) on the Dunkl-harmonics, we show that connection coefficients between bases of Dunkl-harmonics diagonalizing certain Abelian subalgebras are multivariate Racah polynomials. By lifting the action of R(n) to the connection coefficients, we identify the action of the Abelian subalgebras with the action of the Racah operators defined by J. S. Geronimo and P. Iliev. Making appropriate changes of basis, one can identify each generator of R(n) as a discrete operator acting on the multivariate Racah polynomials.

Classification of M2-brane 2-torus bundles, U -duality invariance, and type II gauged supergravities

We obtain the complete classification of the inequivalent classes of M2-brane symplectic torus bundles with monodromy in $SL(2,Z)$ and the precise $U$-duality relations among them. There are eight inequivalent classes of bundles whose monodromy groups, at low energies, are in correspondence with the gauging groups of the eight type II gauged supergravities in nine dimensions. Four of those have previously been found, and they correspond to the ``type IIB side.'' We provide the explicit realization of the remaining four classes associated with the ``type IIA side.'' The precise M2-brane $U$-duality relations between the eight inequivalent classes of bundles have allowed us to identify the remaining four. We conjecture that the classes of gaugings---classifying the eight types of II gauged supergravity in nine dimensions---are determined by the inequivalent coinvariant classes associated with the base and the fiber of the supermembrane bundles and their duals.

Biochemical Szilard engines for memory-limited inference

By designing and leveraging an explicit molecular realisation of a measurement-and-feedback-powered Szilard engine, we investigate the extraction of work from complex environments by minimal machines with finite capacity for memory and decision-making. Living systems perform inference to exploit complex structure, or correlations, in their environment, but the physical limits and underlying cost/benefit trade-offs involved in doing so remain unclear. To probe these questions, we consider a minimal model for a structured environment—a correlated sequence of molecules—and explore mechanisms based on extended Szilard engines for extracting the work stored in these non-equilibrium correlations. We consider systems limited to a single bit of memory making binary ‘choices’ at each step. We demonstrate that increasingly complex environments allow increasingly sophisticated inference strategies to extract more free energy than simpler alternatives, and argue that optimal design of such machines should also consider the free energy reserves required to ensure robustness against fluctuations due to mistakes.

Magnetic quivers, Higgs branches and 6d mathcal{N} = left(1,kern0.5em 0right) theories

The physics of M5 branes placed near an M9 plane on an A-type ALE singularity exhibits a variety of phenomena that introduce additional massless degrees of freedom. There are tensionless strings whenever two M5 branes coincide or whenever an M5 brane approaches the M9 plane. These systems do not admit a low-energy Lagrangian description so new techniques are desirable to shed light on the physics of these phenomena. The 6-dimensional mathcal{N} = left(1,kern0.5em 0right) world-volume theory on the M5 branes is composed of massless vector, tensor, and hyper multiplets, and has two branches of the vacuum moduli space where either the scalar fields in the tensor or hyper multiplets receive vacuum expectation values. Focusing on the Higgs branch of the low-energy theory, previous works suggest the conjecture that a new Higgs branch arises whenever a BPS-string becomes tensionless. Consequently, a single theory admits a multitude of Higgs branches depending on the types of tensionless strings in the spectrum. The two main phenomena discrete gauging and small E8instanton transition can be treated in a concise and effective manner by means of Coulomb branches of 3-dimensional mathcal{N} = 4 gauge theories. In this paper, a formalism is introduced that allows to derive a novel object from a brane configuration, called the magnetic quiver. The main features are as follows: (i) the 3d Coulomb branch of the magnetic quiver yields the Higgs branch of the 6d system, (ii) all discrete gauging and E8 instanton transitions have an explicit brane realisation, and (iii) exceptional symmetries arise directly from brane configurations. The formalism facilitates the description of Higgs branches at finite and infinite gauge coupling as spaces of dressed monopole operators.

Light-front bootstrap for Chern-Simons matter theories

We propose a new approach to solve conformal field theories and apply it to Chern-Simons Matter theories and three-dimensional bosonization duality. All three-point correlation functions of single-trace operators are obtained in the large-N as a simple application. The idea is to construct, as an effective weakly-coupled theory, a nonlinear realization of the conformal algebra in terms of physical, gauge-invariant, operators. The efficiency of the method is also in the use of an analog of the light-cone gauge and of the momentum-space on the CFT side. AdS/CFT is used as a convenient regulator and as a source of the canonical bracket. The uniqueness of the nonlinear realization manifests the three-dimensional bosonization duality at this order. We also find two more non-unitary solutions which should be analogous to the fishnet theories. The results can also be viewed as an explicit realization of the slightly-broken higher spin symmetry.As a by-product, the cubic action of the Higher Spin Gravity in AdS4 is constructed. While generic Higher Spin Gravities are obstructed at higher orders by nonlocality, we point out the existence of two especially simple and well-defined theories: chiral and anti-chiral whose three-point functions correspond to the two new solutions. These two theories are supposed to give a quantum complete and local example of gravitational bulk duals.

Extended supersymmetric multiparticle Euler–Calogero–Moser model

We review the construction of supersymmetric extension of the n-particle Euler–Calogero–Moser model within the Hamiltonian approach [1]. The main feature of the proposed supersymmetrization method is that it is automatically adapted for a model with an arbitrary even number of supersymmetries. It is shown that the number of fermions that must be used in this construction is . We demonstrate that the resulting supersymmetric system is dynamically invariant with respect to the superconformal group and give the explicit realization of its generators in terms of the conserved currents. For the simplest case of the supersymmetric n-particle Euler–Calogero–Moser model we provide its description in superspace by using the corresponding constrained superfields.

Index pairings for Rn-actions and Rieffel deformations

With an action α of Rn on a C∗-algebra A and a skew-symmetric n×n matrix Θ, one can consider the Rieffel deformation AΘ of A, which is a C∗-algebra generated by the α-smooth elements of A with a new multiplication. The purpose of this article is to obtain explicit formulas for K-theoretical quantities defined by elements of AΘ. We give an explicit realization of the Thom class in KK in any dimension n and use it in the index pairings. For local index formulas we assume that there is a densely defined trace on A, invariant under the action. When n is odd, for example, we give a formula for the index of operators of the form PπΘ(u)P, where πΘ(u) is the operator of left Rieffel multiplication by an invertible element u over the unitization of A and P is the projection onto the nonnegative eigenspace of a Dirac operator constructed from the action α. The results are new also for the undeformed case Θ=0. The construction relies on two approaches to Rieffel deformations in addition to Rieffel’s original one: Kasprzak deformation and warped convolution. We end by outlining potential applications in mathematical physics.

Velocity Dependence from Resonant Self-Interacting Dark Matter.

The dark matter density distribution in small-scale astrophysical objects may indicate that dark matter is self-interacting, while observations from clusters of galaxies suggest that the corresponding cross section depends on the velocity. Using a model-independent approach, we show that resonant self-interacting dark matter can naturally explain such a behavior. In contrast to what is often assumed, this does not require a light mediator. We present explicit realizations of this mechanism and discuss the corresponding astrophysical constraints.

Deformation of axion potentials: Implications for spontaneous baryogenesis, dark matter, and isocurvature perturbations

We show that both the baryon asymmetry of the universe and dark matter (DM) can be accounted for by the dynamics of a single axion-like field. In this scenario, the observed baryon asymmetry is produced through spontaneous baryogenesis---driven by the early evolution of the axion---while its late-time coherent oscillations explain the observed DM abundance. Typically, spontaneous baryogenesis via axions is only successful in regions of parameter space where the axion is relatively heavy, rendering it highly unstable and unfit as a dark matter candidate. However, we show that a field-dependent wavefunction renormalization can arise which effectively "deforms" the axion potential, allowing for efficient generation of baryon asymmetry while maintaining a light and stable axion. Meanwhile, such deformations of the potential induce non-trivial axion dynamics, including a tracking behavior during its intermediate phase of evolution. This attractor-like dynamics dramatically reduces the sensitivity of the axion relic abundance to initial conditions and naturally suppresses DM isocurvature perturbations. Finally, we construct an explicit model realization, using a continuum-clockwork axion, and survey the details of its phenomenological viability.