In this paper, we construct the supersymmetric spinning polynomials. These are orthogonal polynomials that serve as an expansion basis for the residue or discontinuity of four-point scattering amplitudes, respecting four-dimensional super Poincare invariance. The polynomials are constructed by gluing on-shell supersymmetric three-point amplitudes of one massive two massless multiplets, and are identified with algebraic Jacobi-polynomials. Equipped with these we construct the supersymmetric EFThedron, which geometrically defines the allowed region of Wilson coefficients respecting UV unitarity and super Poincare invariance.
We construct nontopological solitonic solutions in (3+1)-dimensional Minkowski spacetime carrying a conserved global U(1) charge and nonvanishing angular momentum in a supersymmetric extension of the standard model with low-energy, gauge-mediated symmetry breaking.
We construct SU$(2|1)$, $d=1$ supersymmetric models based on the coupling of dynamical and semi-dynamical (spin) multiplets, where the interaction term of both multiplets is defined on the generalized chiral superspace. The dynamical multiplet is defined as a chiral multiplet ${\bf (2,4,2)}$, while the semi-dynamical multiplet is associated with a multiplet ${\bf (4,4,0)}$ of the mirror type.
We analyze the localization equations relevant to the quantum entropy of spinning supersymmetric black holes in five-dimensional asymptotically flat space. The precise problem is to classify all solutions to the off-shell supersymmetry equations in N=2 supergravity coupled to $n_\text{v}+1$ vector multiplets around the near-horizon black hole. We rewrite these equations in terms of the bosonic spinor bilinears that exist in the geometry for an arbitrary background. We then focus on the vector multiplet fluctuations around the near-horizon attractor region of the supersymmetric black hole, and …
We study the Dirac propagator dressed by an arbitrary number $N$ of photons by means of a worldline approach, which makes use of a supersymmetric ${\cal N} = 1$ spinning particle model on the line, coupled to an external Abelian vector field. We obtain a compact off-shell master formula for the tree level scattering amplitudes associated to the dressed Dirac propagator. In particular, unlike in other approaches, we express the particle fermionic degrees of freedom using a coherent state basis, and consider the gauging of the supersymmetry, which ultimately amounts to integrating over a worldli…
We construct a family of multi-dyonically charged and rotating supersymmetric AdS$_2\times Σ$ solutions of $D=4$, $\mathcal{N}=4$ gauged supergravity, where $Σ$ is a sphere with two conical singularities known as a spindle. We argue that these arise as near horizon limits of extremal dyonically charged rotating and accelerating supersymmetric black holes in AdS$_4$, that we conjecture to exist. We demonstrate this in the non-rotating limit, constructing the accelerating black hole solutions and showing that the non-spinning spindle solutions arise as the near horizon limit of the supersymmetri…
A review of the construction of a Weyl-invariant spinning-membrane action that is $polynomial$ in the fields, without a cosmological constant term, comprised of quadratic and quartic-derivative terms, and where supersymmetry is linearly realized, is presented. The action is invariant under a $modified$ supersymmetry transformation law which is derived from a new $ Q + K + S $ sum-rule based on the 3D-superconformal algebra .
A $q$-deformed free spinning relativistic particle is discussed in the framework of the Lagrangian formalism. Three equivalent Lagrangians are obtained for this system which are endowed with $q$-deformed local (super)gauge symmetries and reparametrization invariance. It is demonstrated that these symmetries are on-shell equivalent only for $ q = \pm1 $ under particular identification of the transformation parameters. The same condition ($ q=\pm1 $) emerges due to the requirement that the $q$-commutator of two supersymmetric gauge transformations should generate a reparametrization plus a super…
We consider particlelike solutions to supergravity based on the Kerr-Newman black hole (BH) solution. The BH singularity is regularized by means of a phase transition to a new vacuum state near the core region confining a dual gauge field. Supersymmetric BPS-saturated domain wall model is suggested which can provide this phase transition and formation the stable charged superconducting core. For spinning particle the core takes the form of thin, relativistically rotaiting disk.
We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. A novel feature of our present investigation is the consistent and clear supersymmetric modification of the celebrated horizontality condition for the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our theory which is considered on a (1, 2)-dimension…
${\rm SU}(2|1)$ supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an $\mathcal{N}{=}\,4$ supersymmetrization of the quantum ${\rm U}(2)$ spin Calogero-Moser model, with an intrinsic mass parameter coming from the centrally-extended superalgebra $\widehat{su}(2|1)$. The full system admits an ${\rm SU}(2|1)$ covariant separation into the center-of-mass sector and the quotient. We derive explicit expressions for the classical and quantum ${\rm SU}(2|1)$ generators in both sectors as well as for the total…
Minimal N=1/2 supersymmetric extension of bosonic Polyakov's string is constructed. This model is natural generalization of Di Vecchia-Ravndal superparticle. The classical sector of the model is investigated, Noether currents and Virosoro supercondition are found. Minimal spinning string is more simple, than the standard N=1 spinning string of Neveu-Schwarz-Ramond and has a number of unusial properties such as a chiral symmetry, parabolic type of equations of movement, non-triviality fermionic sectors for closed strings only and e.t.c.
We construct the action of a relativistic spinning particle from a non-linear realization of a space-time odd vector extension of the Poincaré group. For particular values of the parameters appearing in the lagrangian the model has a gauge world-line supersymmetry.{As a consequence of this local symmetry there are BPS solutions in the model preserving 1/5 of the supersymmetries.} A supersymmetric invariant quantization produces two decoupled 4d Dirac equations.
Peng Huanwu Center for Fundamental Theory（彭桓武理论研究中心）；Centre for Strings, Gravitation and Cosmology, Department of Physics, Indian Institute of Technology Madras（印度马德拉斯理工学院物理学院弦、引力和宇宙学中心）；Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学理论交叉研究中心）；Chennai Mathematical Institute（金奈数学研究所）
We construct a spinning particle that reproduces the propagation of the graviton on those curved backgrounds which solve the Einstein equations, with or without cosmological constant, i.e. Einstein manifolds. It is obtained by modifying the N=4 supersymmetric spinning particle by relaxing the gauging of the full SO(4) R-symmetry group to a parabolic subgroup, and selecting suitable Chern-Simons couplings on the worldline. We test it by computing the correct one-loop divergencies of quantum gravity in D=4.
We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the exchange of symmetric traceless primaries, we generalize the Mellin transform for scalar case to introduce discrete Mellin variables for incorporating spin degrees of freedom. Based on the structures about spinning three and four point Witten diagrams, we also obtain a generalization of the Mack polynomial which can be regarded as a natural kinematical polyn…
New models of the SU(2|1) supersymmetric mechanics based on gauging the systems with dynamical (1,4,3) and semi-dynamical (4,4,0) supermultiplets are presented. We propose a new version of SU(2|1) harmonic superspace approach which makes it possible to construct the Wess-Zumino term for interacting (4,4,0) multiplets. A new N=4 extension of d=1 Calogero-Moser multiparticle system is obtained by gauging the U(n) isometry of matrix SU(2|1) harmonic superfield model.
We construct spinning black hole solutions in five dimensions that take into account the mixed gauge-gravitational Chern-Simons term and its supersymmetric completion. The resulting entropy formula is discussed from several points of view. We include a Taub-NUT base space in order to test recent conjectures relating 5D black holes to 4D black holes and the topological string. Our explicit results show that certain charge shifts have to be taken into account for these relations to hold. We also compute corrections to the entropy of black rings in terms of near horizon data.
We study N=4 super Yang Mills theory at finite U(1)_R charge density (and temperature) using the AdS/CFT Correspondence. The ten dimensional backgrounds around spinning D3 brane configurations split into two classes of solution. One class describe spinning black holes and have previously been extensively studied, and interpreted, in a thermodynamic context, as the deconfined high density phase of the dual field theory. The other class have naked singularities and in the supersymmetric limit are known to correspond to multi-centre solutions describing the field theory in the Coulomb phase. We p…
The problem of a regular matter source for the Kerr spinning particle is discussed. A class of minimal deformations of the Kerr-Newman solution is considered obeying the conditions of regularity and smoothness for the metric and its matter source. It is shown that for charged source corresponding matter forms a rotating bag-like core having (A)dS interior and smooth domain wall boundary. Similarly, the requirement of regularity of the Kerr-Newman electromagnetic field leads to superconducting properties of the core. We further consider the U(I) x U'(I) field model (which was used by Witten to …
We provide a systematic method to compute tree-level scattering amplitudes with spinning external states from amplitudes with scalar external states in arbitrary spacetime dimensions. We write down analytic answers for various scattering amplitudes, including the four graviton amplitude due to the massive spin $J$ exchange. We verify the results by computing angular distributions in 3 + 1 dimensions using various identities involving Jacobi polynomials.
A new local world volume supersymmetric Lagrangian for the bosonic membrane is presented. The starting Lagrangian is the one constructed by Dolan and Tchrakian with vanishing cosmological constant, with quadratic and quartic derivative terms. Our Lagrangian differs from the one constructed by Lindstrom and Rocek in the fact that it is polynomial in the fields facilitating the quantization process. It is argued, rigorously, that if one wishes to construct polynomial actions without a curvature scalar term and, where supersymmetry is linearly realized in the space of physical fields, after the e…
We conjecture that for superconformal field theories in even dimensions, the supersymmetric Casimir energy on a space with topology $S^1\times S^{D-1}$ is equal to an equivariant integral of the anomaly polynomial. The equivariant integration is defined with respect to the Cartan subalgebra of the global symmetry algebra that commutes with a given supercharge. We test our proposal extensively by computing the supersymmetric Casimir energy for large classes of superconformal field theories, with and without known Lagrangian descriptions, in two, four and six dimensions.
We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional N= 2 supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kaehler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generating special holonomy transformations. (An interesting byp…
This paper is concerned with theories describing spinning particles that are formulated in terms of actions possessing either local world-line supersymmetry or local fermionic {\it kappa} invariance. These classical actions are obtained by adding a finite number of spinor or vector coordinates to the usual space-time coordinates. Generalizing to superspace leads to corresponding types of \lq spinning superparticle' theories in which the wave-functions are superfields in some (generally reducible) representation of the Lorentz group. A class of these spinning superparticle actions possesses the…
It has been recently argued by some authors that is impossible to construct a Weyl invariant spinning membrane action, where the $S$-supersymmetry associated with the 3D superconformal algebra, is relinquished without gauge fixing. Contrary to those assertions, we show why it is possible to construct a Weyl-invariant spinning polynomial membrane action, without curvature terms,where $both$ the conformal boost symmetry and $S$-supersymmetry are explicitly broken by the action. It is shown that the gauge algebra $closes$ despite that the two latter symmetries are broken . For this to happen, a m…
Starting from the leading soft term of the 5-point amplitude, involving a graviton and two Kerr black holes, that factorises into the product of the elastic amplitude without the graviton and the leading soft factor, we compute the infrared divergent contribution to the imaginary part of the two-loop eikonal. Then, using analyticity and crossing symmetry, we determine the radiative contribution to the real part of the two-loop eikonal and from it the radiative part of the deflection angle for spins aligned to the orbital angular momentum, the loss of angular momentum and the zero frequency lim…
New kinds of supersymmetry arise in supersymmetric $\sg$-models describing the motion of spinning point-particles in classical backgrounds, for example black-holes, or the dynamics of monopoles. Their geometric origin is the existence of Killing-Yano tensors. The relation between these concepts is explained and examples are given. --- Contribution to Proceedings Quarks-94; Vladimir, Russia (1994).
't Hooft anomalies are known to induce specific contributions to the effective action at finite temperature. We present a general method to directly calculate such contributions from the anomaly polynomial of a given theory, including a term which involves a $U(1)$ connection for the thermal circle isometry. Based on this observation, we show that the asymptotic behavior of the superconformal index of $4d$ $\mathcal{N}=1$ theories on the "second sheet" can be calculated by integrating the anomaly polynomial on a particular background. The integration is then performed by an equivariant method …
We construct various exact analytical solutions of the $SO(3)$ BMN matrix model that correspond to rotating fuzzy spheres and rotating fuzzy tori.These are also solutions of Yang Mills theory compactified on a sphere times time and they are also translationally invariant solutions of the $\mathcal{N} = 1^*$ field theory with a non-trivial charge density. The solutions we construct have a $\mathbb{Z}_N$ symmetry, where $N$ is the rank of the matrices. After an appropriate ansatz, we reduce the problem to solving a set of polynomial equations in $2N$ real variables. These equations have a discre…
The supersymmetric collective field theory with the potential $v'(x)=ωx-{η\over x}$ is studied, motivated by the matrix model proposed by Jevicki and Yoneya to describe two dimensional string theory in a black hole background. Consistency with supersymmetry enforces a two band solution. A supersymmetric classical configuration is found, and interpreted in terms of the density of zeros of certain Laguerre polynomials. The spectrum of the model is then studied and is seen to correspond to a massless scalar and a majorana fermion. The $x$ space eigenfunctions are constructed and expressed in term…
A closed formula of the universal part of supersymmetric Rényi entropy $S_q$ for six-dimensional $(1,0)$ superconformal theories is proposed. Within our arguments, $S_q$ across a spherical entangling surface is a cubic polynomial of $ν=1/q$, with $4$ coefficients expressed as linear combinations of the 't Hooft anomaly coefficients for the $R$-symmetry and gravitational anomalies. As an application, we establish linear relations between the $c$-type Weyl anomalies and the 't Hooft anomaly coefficients. We make a conjecture relating the supersymmetric Rényi entropy to an equivariant integral of…
We give a review of the works devoted to the treatment of the Kerr super black hole solution as a spinning particle. The real, complex and stringy structures of the Kerr and super-Kerr geometries are discussed, as well as the recent results on the regular matter source for the Kerr spinning particle. It is shown that the source has to represent a rotating bag-like bubble having (A)dS interior and a smooth domain wall boundary. The given by Morris supersymmetric generalization of the U(I) x U'(I) field model (which was used by Witten to describe cosmic superconducting strings) is considered, an…
We present an algebraic construction of the orthogonal eigenfunctions of the supersymmetric extension of the rational Calogero-Moser-Sutherland model with harmonic confinement. These eigenfunctions are the superspace extension of the generalized Hermite (or Hi-Jack) polynomials. The conserved quantities of the rational supersymmetric model are related to their trigonometric relatives through a similarity transformation. This leads to a simple expression between the corresponding eigenfunctions: the generalized Hermite superpolynomials are written as a differential operator acting on the corres…
We provide a study of the supersymmetric Adler--Bardeen anomaly in the $\N=1, d=4,6,10$ super-Yang--Mills theories. We work in the component formalism that includes shadow fields, for which Slavnov--Taylor identities can be independently set for both gauge invariance and supersymmetry. We find a method with improved descent equations for getting the solutions of the consistency conditions of both Slavnov--Taylor identities and finding the local field polynomials for the standard Adler--Bardeen anomaly and its supersymmetric counterpart. We give the explicit solution for the ten-dimensional cas…
The Calogero-Sutherland model occurs in a large number of physical contexts, either directly or via its eigenfunctions, the Jack polynomials. The supersymmetric counterpart of this model, although much less ubiquitous, has an equally rich structure. In particular, its eigenfunctions, the Jack superpolynomials, appear to share the very same remarkable combinatorial and structural properties as their non-supersymmetric version. These super-functions are parametrized by superpartitions with fixed bosonic and fermionic degrees. Now, a truly amazing feature pops out when the fermionic degree is suf…
We construct a mathematical framework for twisted N=2 supersymmetric topological quantum field theory on a 4-manifold. Supersymmetry in flat space is defined and the twist homomorphism is constructed, giving us a supermanifold that is the total space of an odd vector bundle over the even 4-manifold. A special category of connections on this space is defined and a decomposition into so-called component fields is proved. The twisted supersymmetric action is computed, and the structure of the action, the decomposition, and the action of a special odd vector field are all shown to have a rich geom…
Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy of quantum syste…
We systematically study the renormalizable three-term polynomial inflation in the supersymmetric and non-supersymmetric models. The supersymmetric inflaton potentials can be realized in supergravity theory, and only have two independent parameters. We show that the general renormalizable supergravity model is equivalent to one kind of our supersymmetric models. We find that the spectral index and tensor-to-scalar ratio can be consistent with the Planck and BICEP2 results, but the running of spectral index is always out of the $2σ$ range. If we do not consider the BICEP2 experiment, these infla…
We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are tensors or spinor-tensors on the curved background while conserved charges correspond to the various differential geometry operators acting on these. The Hamiltonian generalizes Lichnerowicz's wave/Laplace operator. It is central, and the models are supersymmetric whenever the bac…
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 provide a succinct way to construct the supersymmetric completion of $R^n$ $(n\ge3)$ in components using superconformal formulation of old minimal supergravity. As a consequence, we obtain the polynomial $f(R)$ supergravity extending the supersymmetric Starobinsky model to any higher power of $R$. The supersymmetric vacua in polynomial $f(R)$ supergravity are studied. We also present the $R^n$ extended Minimal Volkov-Akulov-Starobinsky Model.
We give a simple description of the classical moduli space of vacua for supersymmetric gauge theories with or without a superpotential. The key ingredient in our analysis is the observation that the lagrangian is invariant under the action of the complexified gauge group $\Gc$. From this point of view the usual $D$-flatness conditions are an artifact of Wess--Zumino gauge. By using a gauge that preserves $\Gc$ invariance we show that every constant matter field configuration that extremizes the superpotential is $\Gc$ gauge-equivalent (in a sense that we make precise) to a unique classical vac…
We analyze the ground state of a strongly interacting fermion chain with a supersymmetry. We conjecture a number of exact results, such as a hidden duality between weak and strong couplings. By exploiting a scale free property of the perturbative expansions, we find exact expressions for the order parameters, yielding the critical exponents. We show that the ground state of this fermion chain and another model in the same universality class, the XYZ chain along a line of couplings, are both written in terms of the same polynomials. We demonstrate this explicitly for up to N = 24 sites, and pro…
By using the technique of supersymmetric quantum mechanics, we study a quasi exactly solvable extension of the N-particle rational Calogero model with harmonic confining interaction. Such quasi exactly solvable many particle system, whose effective potential in the radial direction yields a supersymmetric partner of the radial harmonic oscillator, is constructed by including new long-range interactions to the rational Calogero model. An infinite number of bound state energy levels are obtained for this system under certain conditions. We also calculate the corresponding bound state wave functi…
We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding topological quantum field theory, and it turns out that they can be expressed in terms of Seiberg-Witten invariants. In this analysis we use recent exact results on the moduli space of vacua of the untwisted $N=1$ and $N=2$ supersymmetric counterparts of the topological quantum field theory under consideration, as well as on electric-magnetic duality for $N=2…
Making use of integral forms and superfield techniques we propose supersymmetric extensions of the multimetric gravity Lagrangians in dimensions one, two, three and four. The supersymmetric interaction potential covariantly deforms the bosonic one, producing in particular suitable super-symmetric polynomials generated by the Berezinian. As an additional application of our formalism we construct supersymmetric multi-Maxwell theories in dimensions three and four.
It is shown that the higher order supersymmetric partners of the harmonic oscillator Hamiltonian provide the simplest non-trivial realizations of the polynomial Heisenberg algebras. A linearized version of the corresponding annihilation and creation operator leads to a Fock representation which is the same as for the harmonic oscillator Hamiltonian
We derive the necessary and sufficient condition for Type A N-fold supersymmetry by direct calculation of the intertwining relation and show the complete equivalence between this analytic construction and the sl(2) construction based on quasi-solvability. An intimate relation between the pair of algebraic Hamiltonians is found. The classification problem on Type A N-fold supersymmetric models is investigated by considering the invariance of both the Hamiltonians and N-fold supercharge under the GL(2,K) transformation. We generalize the Bender-Dunne polynomials to all the Type A N-fold supersym…
A new generalization of the Jack polynomials that incorporates fermionic variables is presented. These Jack superpolynomials are constructed as those eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland (CMS) model that decomposes triangularly in terms of the symmetric monomial superfunctions. Many explicit examples are displayed. Furthermore, various new results have been obtained for the supersymmetric version of the CMS models: the Lax formulation, the construction of the Dunkl operators and the explicit expressions for the conserved charges. The ref…
