Developing a non-compact version of the SUSY Hopf map, we formulate the quantum Hall effect on a super-hyperboloid. Based on $OSp(1|2)$ group theoretical methods, we first analyze the one-particle Landau problem, and successively explore the many-body problem where Laughlin wavefunction, hard-core pseudo-potential Hamiltonian and topological excitations are derived. It is also shown that the fuzzy super-hyperboloid emerges in the lowest Landau level.
Novel $\mathcal{N}{=}\,2$ and $\mathcal{N}{=}\,4$ supersymmetric extensions of the Calogero-Sutherland hyperbolic systems are obtained by gauging the ${\rm U}(n)$ isometry of matrix superfield models. The bosonic core of the $\mathcal{N}{=}\,2$ models is the standard $A_{n-1}$ Calogero-Sutherland hyperbolic system, whereas the ${\mathcal N}{=}\,4$ model contains additional semi-dynamical spin variables and is an extension of the U(2) spin Calogero-Sutherland hyperbolic system. We construct two different versions of the ${\mathcal N}{=}\,4$ model, with and without the interacting center-of-mass…
We develop a supersymmetric extension of Chern-Simons theory and Chern-Simons-Landau-Ginzburg theory for supersymmetric quantum Hall liquid. Supersymmetric counterparts of topological and gauge structures peculiar to the Chern-Simons theory are inspected in the supersymmetric Chern-Simons theory. We also explore an effective field theoretical description for the supersymmetric quantum Hall liquid. The key observation is the the charge-flux duality. Based on the duality, we derive a dual supersymmetric Chern-Simons-Landau-Ginzburg theory, and discuss physical properties of the topological excit…
Supersymmetric quantum Hall liquids are constructed on a supersphere in a supermonopole background. We derive a supersymmetric generalization of the Laughlin wavefunction, which is a ground state of a hard-core $OSp(1|2)$ invariant Hamiltonian. We also present excited topological objects, which are fractionally charged deficits made by super Hall currents. Several relations between quantum Hall systems and their supersymmetric extensions are discussed.
The $\mathcal{N}{=}\,4$ supersymmetric $\mathrm{U}(2)$-spin hyperbolic Calogero-Sutherland model with odd matrix fields is examined. Explicit form of the $\mathcal{N}{=}\,4$ supersymmetry generators is derived. The Lax representation for the dynamics of the $\mathcal{N}{=}\,4$ hyperbolic $\mathrm{U}(2)$-spin Calogero-Sutherland system is found. The reduction to the $\mathcal{N}{=}\,4$ supersymmetric spinless hyperbolic Calogero-Sutherland system is established.
Starting from the Hamiltonian formulation of supersymmetric Calogero models associated with the classical $A_n$, $B_n$, $C_n$ and $D_n$ series we construct the ${\cal N}{=}\,2$ and ${\cal N}{=}\,4$ supersymmetric extensions of the their hyperbolic/trigonometric Calogero-Sutherland cousins. The bosonic core of these models are the standard Calogero-Sutherland hyperbolic/trigonometric systems.
We revisit the definition of the 6j-symbols from the modular double of U_q(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to qu…
The $\mathcal{N}{=}\,2$ supersymmetric hyperbolic Calogero-Sutherland model obtained in arXiv:1902.08023 by gauging the $\mathcal{N}{=}\,2$ superfield matrix system is studied. Classical and quantum $\mathcal{N}{=}\,2$ supersymmetry generators are found. The difference in the structure of classical and quantum supercharges is established. It is shown that, unlike classical supercharges, quantum supersymmetry generators can be limited to an invariant sub-sector that does not contain off-diagonal fermion operators. The Lax pair for supersymmetric generalization of the hyperbolic Calogero-Sutherl…
We study supersymmetric gauge theories with an R-symmetry, defined on non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a supersymmetry-preserving quotient of Euclidean AdS$_3$. We compute the exact partition function in these theories, using the method of localization, thus reducing the problem to the computation of one-loop determinants around a supersymmetric locus. We evaluate the one-loop determinants employing three different techniques: an index theorem, the method of pairing of eigenvalues, and the heat kernel method. Along the way, we discuss aspects of supe…
The supersymmetric Rényi entropy across a spherical entangling surface in a $d$-dimensional SCFT with flavor defects is equivalent to a supersymmetric partition function on $\mathbb{H}^{d-1} \times \mathbb{S}^1$, which can be computed exactly using localization. We consider the holographically dual BPS solutions in $(d +1)$-dimensional matter coupled supergravity $(d = 3 , 5)$, which are charged hyperbolically sliced AdS black holes. We compute the renormalized on-shell action and the holographic supersymmetric Rényi entropy and show a perfect match with the field theory side. Our setup allows…
Supersymmetric quantum Hall liquids are constructed on a noncommutative superplane. We explore a supersymmetric formalism of the Landau problem. In the lowest Landau level, there appear spin-less bosonic states and spin-1/2 down fermionic states, which exhibit a super-chiral property. It is shown the Laughlin wavefunction and topological excitations have their superpartners. Similarities between supersymmetric quantum Hall systems and bilayer quantum Hall systems are discussed.
We study both the continuous model and the discrete model of the integer quantum Hall effect on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper [CHMM]. Here we model impurities, that is we consider the effect of a random or almost periodic potential as opposed to just periodic potentials. The Hall conductance is identified as a geometric invariant associated to an algebra of observables, which has plateaus at gaps in extended states of the Hamiltonian. We use the Fredholm modules defined in [CHMM] to prove the integrality of the Hall conductance in t…
It is argued that there are strong similarities between the infra-red physics of N=2 supersymmetric Yang-Mills and that of the quantum Hall effect, both systems exhibit a hierarchy of vacua with a sub-group of the modular group mapping between them. The scaling flow for pure SU(2) N=2 supersymmetric Yang-Mills in 4-dimensions is re-examined and an earlier suggestion in the literature, that was singular at strong coupling, is modified to a form that is well behaved at both weak and strong coupling and describes the crossover in an analytic fashion. Similarities between the phase diagram and the…
We develop a supersymmetric extension of the Susskind-Polychronakos matrix theory for the quantum Hall fluids. This is done by considering a system combining two sets of different particles and using both a component field method as well as world line superfields. Our construction yields a class of models for fractional quantum Hall systems with two phases U and D involving, respectively $N_1$ bosons and $N_2$ fermions. We build the corresponding supersymmetric matrix action, derive and solve the supersymmetric generalization of the Susskind-Polychronakos constraint equations. We show that the…
A supersymmetric Hamiltonian is constructed for the edge excitations of the Moore-Read (Pfaffian) like state, which is a realization of the N=2 supersymmetric CS model. Fermionic generators and their conjugates are introduced to deal with the fermion pairing, whose condensation form a BCS like state. After Bogoliubov transformation, a N=2 supersymmetric and nonrelativistic Hamiltonian is found to take a known form, which is integrable. The main difference between the Moore-Read state and our BCS like state is that the number of fermion pairs in our formalism is not fixed. However, we have also…
The parallel roles of modular symmetry in ${\cal N}=2$ supersymmetric Yang-Mills and in the quantum Hall effect are reviewed. In supersymmetric Yang-Mills theories modular symmetry emerges as a version of Dirac's electric -- magnetic duality. It has significant consequences for the vacuum structure of these theories, leading to a fractal vacuum which has an infinite hierarchy of related phases. In the case of ${\cal N}=2$ supersymmetric Yang-Mills in 3+1 dimensions, scaling functions can be defined which are modular forms of a subgroup of the full modular group and which interpolate between va…
We construct a supersymmetric quantum Hall liquid with a deformed supersymmetry. One parameter is introduced in the supersymmetric Laughlin wavefunction to realize the original Laughlin wavefunction and the Moore-Read wavefunction in two extremal limits of the parameter. The introduced parameter corresponds to the coherence factor in the BCS theory. It is pointed out that the parameter-dependent supersymmetric Laughlin wavefunction enjoys a deformed supersymmetry. Based on the deformed supersymmetry, we construct a pseudo-potential Hamiltonian whose groundstate is exactly the parameter-depende…
In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables. We define a twisted analogue of the Kasparov map, which enables us to use the pairing between $K$-theory and cyclic cohomology theory, to identify this geometric invariant with a topological index, thereby proving the integrality of the Hall conductivity in this case.
This work summarises recent progress obtained by the mini-superpspace quantization of $\mathcal N=1$, $d=4$ supergravity, formulated in the framework of the Bianchi IX cosmological model. The emphasis is put on three main results : the completeness of the solution space obtained, the elements suggesting a hidden Kac-Moody structure of the theory and those leading to conjecture an avoidance of the cosmological singularity by some branches of the wave function of the Universe.
Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasi-exactly solvable PT-symmetric potentials with two known real eigenvalues (the ground state and first-excited state energies). We construct examples, namely those of complexified non-polynomial oscillators and of a complexified hyperbolic potential, to demonstrate how our scheme works in practice. For the former we provide a connection with the sl(2) method, illustrating the comparative advantages of the supersymmetric one.
We consider the matrix model associated with pp-wave background and construct supersymmetric branes. In addition to the spherical membrane preserving 16 supersymmetries, one may construct rotating elliptic membranes preserving 8 supersymmetries. The other branch describes rotating 1/8 BPS hyperbolic branes in general. When the angular momentum vanishes in this branch, the hyperbolic brane becomes 1/4 BPS preserving 8 real supersymmetries. It may have the shape of hyperboloid of one or two sheets embedded in the flat three space. We study the spectrum of the worldvolume fields on the hyperbolic…
We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantise the vortices and, by relating their dynamics to a matrix model, show that their ground state wavefunction is in the same universality class as the Laughlin state. We further construct coherent state representations of the excitations of a finite number of vortices. These are quasi-holes. By an explicit computation of the Berry phase, without resorting to a plasma analogy, we show that these excitation…
The Ruijsenaars-Schneider models are conventionally regarded as relativistic generalizations of the Calogero integrable systems. Surprisingly enough, their supersymmetric generalizations escaped attention. In this work, N=2 supersymmetric extensions of the rational and hyperbolic Ruijsenaars-Schneider three-body models are constructed within the framework of the Hamiltonian formalism. It is also known that the rational model can be described by the geodesic equations associated with a metric connection. We demonstrate that the hyperbolic systems are linked to non-metric connections.
The confluent second-order supersymmetric quantum mechanics, in which the factorization energies tend to a common value, is used to generate Hamiltonians with known spectra departing from the hyperbolic Rosen-Morse and Eckart potentials. The possible spectral modifications, as to create a new level or to delete a given one, as well as the isospectral transformations, are discussed.
Introducing a non-compact version of the Hopf map, we demonstrate remarkable close relations between quantum Hall effect and twistor theory. We first construct quantum Hall effect on a hyperboloid based on the noncompact 2nd Hopf map of split-quaternions. We analyze a hyperbolic one-particle mechanics, and explore many-body problem, where a many-body groundstate wavefunction and membrane-like excitations are derived explicitly. In the lowest Landau level, the symmetry is enhanced from $SO(3, 2)$ to the $SU(2, 2)$ conformal symmetry. We point out that the quantum Hall effect naturally realizes …
In this paper we present a family of supersymmetric Wilson loops of N=4 supersymmetric Yang-Mills theory in Minkowski space. Our examples focus on curves restricted to hyperbolic submanifolds, H_3 and H_2, of space-time. Generically they preserve two supercharges, but in special cases more, including a case which has not been discussed before, of the hyperbolic line, conformal to the straight line and circle, which is half-BPS. We discuss some general properties of these Wilson loops and their string duals and study special examples in more detail. Generically the string duals propagate on a c…
In this paper we give a survey of some models of the integer and fractional quantum Hall effect based on noncommutative geometry. We begin by recalling some classical geometry of electrons in solids and the passage to noncommutative geometry produced by the presence of a magnetic field. We recall how one can obtain this way a single electron model of the integer quantum Hall effect. While in the case of the integer quantum Hall effect the underlying geometry is Euclidean, we then discuss a model of the fractional quantum Hall effect, which is based on hyperbolic geometry simulating the multi-e…
We describe string-theory and $d=11$ supergravity solutions involving symmetric spaces of constant negative curvature. Many examples of non-supersymmetric string compactifications on hyperbolic spaces $H_r$ of finite volume are given in terms of suitable cosets of the form $H_r/Γ$, where $Γ$ is a discrete group. We describe in some detail the cases of the non-compact hyperbolic spaces $F_2$ and $F_3$, representing the fundamental regions of $H_2$ and $H_3$ under $SL(2,Z)$ and the Picard group, respectively. By writing $AdS$ as a U(1) fibration, we obtain new solutions where $AdS_{2p+1}$ gets u…
We analyze the Cauchy problem for the Klein-Gordon equation on the type IIB supergravity backgrounds $AdS^5 \times Y^{p,q}$, where $Y^{p,q}$ is any of the Sasaki-Einstein 5-manifolds recently discovered by Gaunlett, Martelli, Sparks and Waldram (Adv. Theor. Math. Phys. 8 (2004) 711--734). Although these spaces are not globally hyperbolic, we prove that there exists a unique admissible propagator and derive an integral representation thereof using spectral-theoretic techniques.
We study Bailey pairs construction for hyperbolic hypergeometric integral identities acquired via the duality of lens partitions functions for the three-dimensional $\mathcal N=2$ supersymmetric gauge theories on $S_b^3/\mathbb{Z}_r$. The novel Bailey pairs are constructed for the star-triangle relation, the star-star relation and the pentagon identity. The first two of them are integrability conditions for the Ising-type integrable lattice models. The last one corresponds to the representation of the basic $2-3$ Pachner move for triangulated 3-manifolds.
Non-linear sigma models that arise from the supersymmetric approach to disordered electron systems contain a non-compact bosonic sector. We study the model with target space H^2, the two-hyperboloid with isometry group SU(1,1), and prove that in three dimensions moments of the fields are finite in the thermodynamic limit. Thus the non-compact symmetry SU(1,1) is spontaneously broken. The bound on moments is compatible with the presence of extended states.
A class of $AdS_2\times Σ_2$, with $Σ_2$ being a two-sphere or a hyperbolic space, solutions within four-dimensional $N=4$ gauged supergravity coupled to three-vector multiplets with dyonic gauging is identified. The gauged supergravity has non-semisimple $SO(3)\ltimes (\mathbf{T}^3,\hat{\mathbf{T}}^3)$ gauge group and can be obtained from a consistent truncation of eleven-dimensional supergravity on a tri-sasakian manifold. The maximally symmetric vacua contain $AdS_4$ geometries with $N=1,3$ supersymmetry corresponding to $N=1$ and $N=3$ superconformal field theories (SCFTs) in three dimensi…
We consider the spin quantum Hall transition which may occur in disordered superconductors with unbroken SU(2) spin-rotation symmetry but broken time-reversal symmetry. Using supersymmetry, we map a model for this transition onto the two-dimensional percolation problem. The anisotropic limit is an sl(2|1) supersymmetric spin chain. The mapping gives exact values for critical exponents associated with disorder-averages of several observables in good agreement with recent numerical results.
In this paper we prove that the four-dimensional hyperbolic supersymmetric black holes can be unstable in the canonical ensemble. To this end, we work with an infinite class of $\,\mathcal{N}=2$ supergravity theories interpolating between all the single dilaton truncations of the $\mathrm{SO}(8)$ gauged $\,\mathcal{N}=8$ supergravity. Within these models, we study electrically charged solutions of two different kinds: supersymmetric hairy and extremal non-supersymmetric Reissner-Nordström black holes. We consider these solutions within the same canonical ensemble and show that, for suitable ch…
In this work we put forward an effective Gaussian free field description of critical wavefunctions at the transition between plateaus of the integer quantum Hall effect. To this end, we expound our earlier proposal that powers of critical wave intensities prepared via point contacts behave as pure scaling fields obeying an Abelian operator product expansion. Our arguments employ the framework of conformal field theory and, in particular, lead to a multifractality spectrum which is parabolic. We also derive a number of old and new identities that hold exactly at the lattice level and hinge on t…
We present a unified description of the quantum Hall effect in graphene on the basis of the 8-component Dirac Hamiltonian and the supersymmetric (SUSY) quantum mechanics. It is remarkable that the zero-energy state emerges because the Zeeman splitting is exactly as large as the Landau level separation, as implies that the SUSY is a good symmetry. For nonzero energy states, the up-spin state and the down-spin state form a supermultiplet possessing the spin SU(2) symmetry. We extend the Dirac Hamiltonian to include two indices $j_{\uparrow}$ and $j_{\downarrow}$, characterized by the dispersion …
We use the AdS/CFT correspondence to compute a conductivity associated with massive N=2 supersymmetric hypermultiplet fields at finite baryon density, propagating through an N=4 supersymmetric SU(Nc) Yang-Mills plasma in the large Nc, large 't Hooft coupling limit. We do so by introducing external electric and magnetic fields coupled to baryon number and computing the resulting induced current, from which we extract the conductivity tensor. At large hypermultiplet mass we compute the drag force on the charge carriers. We also compute the product of the drag coefficient with the kinetic mass, a…
In this paper, we study $(2+1)$-dimensional quantum anomalous Hall states, i.e. band insulators with quantized Hall conductance, using the exact holographic mapping. The exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in $(3+1)$-dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a $(3+1)$-dimensional topological insulator. The dual description enables a new characterizat…
In [Can et al. 2016], quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic adiabatic states, which we define in the paper. We highlight the connection between the universal features of geometric transport of quantum Hall states and holomorphic dimension of primary fields in conformal field theory. In parallel we compute the universal finite-size corrections to the free energy of a critical system on a hyperbolic sphere with conical and cu…
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra sl(2, C). This extends to the complex domain the well-known relationship between SUSYQM and potential algebras for Hermitian Hamiltonians, resulting from their common link with the factorization method and Darboux transformations. In the same framework, we also generate for the first time a pair of elliptic partner potentials of Weierstrass $\wp$ type, one of them being r…
We present three holographic constructions of fractional quantum Hall effect (FQHE) via string theory. The first model studies edge states in FQHE using supersymmetric domain walls in N=6 Chern-Simons theory. We show that D4-branes wrapped on CP^1 or D8-branes wrapped on CP^3 create edge states that shift the rank or the level of the gauge group, respectively. These holographic edge states correctly reproduce the Hall conductivity. The second model presents a holographic dual to the pure U(N)_k (Yang-Mills-)Chern-Simons theory based on a D3-D7 system. Its holography is equivalent to the level-…
In this paper, we propose a new approach to study the BPS dynamics in N=4 supersymmetric U(N) Yang-Mills theory on R X S^3, in order to better understand the emergence of gravity in the gauge theory. Our approach is based on supersymmetric, space-filling Q-balls with R-charge, which we call R-balls. The usual collective coordinate method for non-topological scalar solitons is applied to quantize the half and quarter BPS R-balls. In each case, a different quantization method is also applied to confirm the results from the collective coordinate quantization. For finite N, the half BPS R-balls wi…
The Moore-Read state is one the most well known non-Abelian fractional quantum Hall states. It supports non-Abelian Ising anyons in the bulk and a chiral bosonic and chiral Majorana modes on the boundary. It has been recently conjectured that these modes are superpartners of each other and described by a supersymmetric conformal field theory [1]. We propose a non-relativistic supergeometric theory that is compatible with this picture and gives rise to an effective spin-3/2 field in the bulk. After breaking supersymmetry through a Goldstino, the spin-3/2 field becomes massive and can be seen as…
D=11 Supergravity near a space-like singularity admits a cosmological billiard description based on the hyperbolic Kac-Moody group E10. The quantization of this system via the supersymmetry constraint is shown to lead to wavefunctions involving automorphic (Maass wave) forms under the modular group W^+(E10)=PSL(2,O) with Dirichlet boundary conditions on the billiard domain. A general inequality for the Laplace eigenvalues of these automorphic forms implies that the wave function of the universe is generically complex and always tends to zero when approaching the initial singularity. We discuss…
We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D=4 simple supergravity for an SO(3)-homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact sub-algebra of the rank-3 h…
Motivated by a recent development in the field theory of the fractional quantum Hall effect, we propose a supersymmetric field theoretical model of quantum critical d-wave and (d+id)-wave superconductors. New concept is a composite particle with the supercharge which is formed by electron (hole) and supersymmetric collective configurations of spin and charge. Quantum critical d-wave superconductor is characterized as the condensate of these composite particles.
We study the physics of probe D6-branes with quantized internal worldvolume flux in the ABJM background with unquenched massless flavors. This flux breaks parity in the (2+1)-dimensional gauge theory and allows quantum Hall states. Parity breaking is also explicitly demonstrated via the helicity dependence of the meson spectrum. We obtain general expressions for the conductivities, both in the gapped Minkowski embeddings and in the compressible black hole ones. These conductivities depend on the flux and contain a contribution from the dynamical flavors which can be regarded as an effect of in…
We construct the c-function whose gradient determines the RG flow of the conductivities (sigma_xy and sigma_xx) for a quantum Hall system, subject to two assumptions. (1) We take the flow to be invariant with respect to the infinite discrete symmetry group, recently proposed by several workers to explain the `superuniversality' of the delocalization exponents in these systems. (2) We also suppose the flow to be `quasi-holomorphic' (which we make precise) in the sense that it is as close as possible to a one-dimensional flow in the complex parameter sigma_xy +i sigma_xx. These assumptions toget…
An N-channel generalization of the network model of Chalker and Coddington is considered. The model for N = 1 is known to describe the critical behavior at the plateau transition in systems exhibiting the integer quantum Hall effect. Using a recently discovered equality of integrals, the network model is transformed into a lattice field theory defined over Efetov's sigma model space with unitary symmetry. The transformation is exact for all N, no saddle-point approximation is made, and no massive modes have to be eliminated. The naive continuum limit of the lattice theory is shown to be a supe…
Two pictures of BPS bound states in Calabi-Yau compactifications of type II string theory exist, one as a set of particles at equilibrium separations from each other, the other as a fusion of D-branes at a single point of space. We show how quiver quantum mechanics smoothly interpolates between the two, and use this, together with recent mathematical results on the cohomology of quiver varieties, to solve some nontrivial ground state counting problems in multi-particle quantum mechanics, including one arising in the setup of the spherical quantum Hall effect, and to count ground state degenera…
We found a quantum cohomology/homology of quantum Hall effect which arises as the invariant property of the Chern-Simons theory of quantum Hall effect and showed that it should be equivalent to the quantum cohomology which arose as the invariant property of topological sigma models. This isomorphism should be related with an equivalence between the supersymmetric- and quantization structures in two dimensional models and/or with an equivalence between topological sigma models and the Chern-Simons theory by the methode of master equation.
We study the quantum fermionic billiard defined by the dynamics of a quantized supersymmetric squashed three-sphere (Bianchi IX cosmological model within D=4 simple supergravity). The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. We focus on the 15- and 20-dimensional subspaces (with fermion numbers N_F=2 and N_F=3) where there exist propagating solutions of the supersymmetry constraints that carry (in the small-wavelength limit) a chaotic spinorial dynamics generalizing the Belinskii-Khalatnikov-Lifshitz classical "oscillatory" dynamics. By…
It is shown that the Calogero-Moser models based on all root systems of the finite reflection groups (both the crystallographic and non-crystallographic cases) with the rational (with/without a harmonic confining potential), trigonometric and hyperbolic potentials can be simply supersymmetrised in terms of superpotentials. There is a universal formula for the supersymmetric ground state wavefunction. Since the bosonic part of each supersymmetric model is the usual quantum Calogero-Moser model, this gives a universal formula for its ground state wavefunction and energy, which is determined pure…
