An overview of hadron spectroscopy obtained from an extension of superconformal field theory of de Alfaro, Fubini and Furlan, which originates from the supergauge transformation of Wess and Zumino and influenced on the string theory are preseted.
The standard model of hadron dynamics is based on gauge theory. In the 4 dimensional ($4D$) QCD Lagrangian, the Faddeev-Popov ghost that appears to compensate unphysical degrees of freedom in internal fermion propagators can be regarded as the partner of a fermion. Donaldson formulated a $5D$ gauge theory.
Fubini and Rabinovici formulated superconformal quantum mechanics in de Sitter space, and Brodsky and de Téramond formulated relativistic light front holographic QCD (LFHQCD) in Kaluza-Klein type $5D$ anti de Sitter (AdS) space, using Dirac's light cone gauge, and succeeded in obtaining spectroscopy of baryons (fermions) and corresponding mesons (bosons), except the pion which is an axial scalar meson that remains massless.
In the LFHQCD, the time parameter $τ=t\pm z/c$, $(z\in {\bf C})$ appears by the choice of the light-cone gauge, or the front form of Dirac's formulation. The theory is an extension of AdS/CFT correspodence of Maldacena in which incorporation of Einstein's gravity theory in Maxwell's electromagnetic theory was tried in the framework of the string theory.
Taking mathematical frameworks of treating the supersymmetry by Brodsky, Witten, Connes and their collaborators as central thema, we summarize other supersymmetric approaches like string theory in particle physics and astrophysics. We discuss about 2 dimensional solitons whose dynamics is represented also by $τ=t\pm z/c$, ($z\in$ pure quaternion${\bf H}$).
Q-balls are a possible feature of any model with a conserved, global U(1) symmetry and no massless, charged scalars. It is shown that for a broad class of models of metastable supersymmetry breaking they are extremely influential on the vacuum lifetime and make seemingly viable vacua catastrophically short lived. A net charge asymmetry is not required as there is often a significant range of parameter space where statistical fluctuations alone are sufficient. This effect is examined for two supersymmetry breaking scenarios. It is found that models of minimal gauge mediation (which necessarily …
We reconsider the gauge hierarchy problem from the viewpoint of effective field theories and a high-energy physics, motivated by the alternative scenario that the standard model holds up to a high-energy scale such as the Planck scale. The problem is restated as the question whether it is possible to construct a low-energy effective theory and the interaction with heavy particles, without spoiling the structure of a high-energy physics supported by an excellent concept. Based on this reinterpretation, we give a conjecture that theories with hidden fermionic symmetries can be free from the gaug…
We investigate a 2-dimensional N=2 supersymmetric model which consists of n chiral superfields with Kahler potential. When we define quantum observables, we are always plagued by operator ordering problem. Among various ways to fix the operator order, we rely upon the supersymmetry. We demonstrate that the correct operator order is given by requiring the super Poincare algebra by carrying out the canonical Dirac bracket quantization. This is shown to be also true when the supersymmetry algebra has a central extension by the presence of topological soliton. It is also shown that the path of sol…
In presence of string solitons, index theorems for the generalised Dirac operators have to be revisited. We show that in supersymmetric configurations the fermionic operators decouple, so that there are no mixing effects between different fermions in the index theorems. We extend the index theorems in presence of torsion to the generic case of manifolds with boundary, which naturally appear in string solutions and apply this result to the soliton solution by Callan, Harvey and Strominger.
We present new classes of string-like soliton solutions in ($N=1$; $D=10$), ($N=2$; $D=6$) and ($N=4$; $D=4$) heterotic string theory. Connections are made between the solution-generating subgroup of the $T$-duality group of the compactification and the number of spacetime supersymmetries broken. Analogous solutions are also noted in ($N=1,2$; $D=4$) compactifications, where a different form of supersymmetry breaking arises.
This talk summarizes our recent work establishing an algebraic, model-independent basis for the existence of \B bounds and \B equations for topologically non-trivial solitons and instantons. Our arguments use supersymmetry in an essential way to understand both supersymmetric and non-supersymmetric theories. Our arguments are constructive and work in nearly any number of dimensions. Presented at and to appear in the proceedings of the XX^{th} International Colloquium on Group Theoretical Methods in Physics, Osaka, July 1994.
We give model-independent arguments, valid in nearly any number of spacetime dimensions, that topological solitons and instantons satisfy Bogomol'nyi-type bounds and, when these bounds are saturated, satisfy self-duality equations. In the supersymmetric case, we also show that, in spacetime dimensions greater than two, theories with topological charges necessarily exhibit extended supersymmetry, in which the topological charge appears as the central charge. The significance of our arguments lies in their generality. In the supersymmetric case, we obtain insight into the contrast observed betwe…
22 years ago, Rebhan and van Nieuwenhuizen showed that loop corrections to the mass of a quantum soliton depend on a choice of matching condition for the regulators of the vacuum and one-soliton sector Hamiltonians. In supersymmetric theories, regulators which preserve supersymmetry yield the correct quantum corrections, as these are dictated by supersymmetry. However, in a general theory it is not known which matching condition yields the correct mass. We use the leading term in the operator that creates the soliton to construct the regulated one-soliton sector Hamiltonian from that of the va…
We investigate BPS properties of the charged soliton solutions of D-brane worldvolume theory, which is described by the supersymmetric Dirac-Born-Infeld action, by means of the N=2 target-space supersymmetry algebra. Our results agree with those obtained previously. We also extend our BPS analysis to the case where axion background exists.
We demonstrate an unambiguous and robust method for computing fermionic corrections to the energies of classical background field configurations. We consider the particular case of a sequence of background field configurations that interpolates continuously between the trivial vacuum and a widely separated soliton/antisoliton pair in 1+1 dimensions. Working in the continuum, we use phase shifts, the Born approximation, and Levinson's theorem to avoid ambiguities of renormalization procedure and boundary conditions. We carry out the calculation analytically at both ends of the interpolation and…
The $N=2$ fermionic string theory is revisited in light of its recently proposed equivalence to the non-compact $N=4$ fermionic string model. The issues of space-time Lorentz covariance and supersymmetry for the BRST quantized $N=2$ strings living in uncompactified $2 + 2$ dimensions are discussed. The equivalent local quantum supersymmetric field theory appears to be the most transparent way to represent the space-time symmetries of the extended fermionic strings and their interactions. Our considerations support the Siegel's ideas about the presence of $SO(2,2)$ Lorentz symmetry as well as a…
We reexamine the issue of the soliton mass in two-dimensional models with N =1 supersymmetry. The superalgebra has a central extension, and at the classical level the soliton solution preserves 1/2 of supersymmetry which is equivalent to BPS saturation. We prove that the property of BPS saturation, i.e. the equality of the soliton mass to the central charge, remains intact at the quantum level in all orders of the weak coupling expansion. Our key finding is an anomaly in the expression for the central charge. The classical central charge, equal to the jump of the superpotential, is amended by …
Using world line fermions $Υ_{\pm}^{m}=Υ_{\pm}^{m}(τ) $ valued in vector representation of $SO(d,4-d) $ with $d=2,3,4,$ we develop a pure fermionic analog of Penrose twistor construction. First, we show that Fermi antisymmetry requiring $(Υ_{\pm}^{m}) ^{2}=0$ can be solved by using twistor like variables. Then we study the corresponding dual twistor like field action and show that quantum spectrum exhibits naturally 4D $\mathcal{N}=1$ target space supersymmetry. Higher spin world line field solutions of the constraint $(Π_{s}^{m}) ^{2}=0$, $s\in \mathbb{Z}$ are also discussed.
We present a simple algorithm to implement the generalized derivative expansion introduced previously by L-H. Chan, and apply it to the calculation of the one-loop mass correction to the classical soliton mass in the 1+1 dimensional Jacobi model. We then show how this derivative expansion approach implies that the total (bosonic plus fermionic) mass correction in an N=1 supersymmetric soliton model is determined solely by the asymptotic values (and derivatives) of the fermionic background potential. For a static soliton the total mass correction is $-m/(2π)$, in agreement with recent analyses …
We study two fermionic systems that have an underlying supersymmetric structure, namely a color superconductor and Dirac fermion in a Reissner-Nordström-anti-de Sitter gravitational background. In the chiral limit of the color superconductor, the localized fermionic zero modes around the vortex form an N=2 with zero central charge $d=1$ quantum algebra, with all the operators being Fredholm. We compute the Witten index of this algebra and we find an unbroken supersymmetry. The fermionic gravitational system in the chiral limit too, has two underlying unbroken N=2, $d=1$ supersymmetric algebras…
The large N limit of fermionic vectors models is studied using bilocal variables, in the framework of a collective field theory approach. The large N configuration is determined completely using only classical solutions of the model. Further, the Bethe-Salpeter equations of the model are cast as a Green's function problem. One of the main results of this work is to show that this Green's function is in fact the large N bilocal itself.
We investigate the microphysics of cosmic strings in Nonabelian gauge theories with N=1 supersymmetry. We give the vortex solutions in a specific example and demonstrate that fermionic superconductivity arises because of the couplings and interactions dictated by supersymmetry. We then use supersymmetry transformations to obtain the relevant fermionic zero modes and investigate the role of soft supersymmetry breaking on the existence and properties of the superconducting strings.
The excitations referred to as oscillons are long-lived time-dependent field configurations which emerge dynamically from non-linear field theories. Such long-lived solutions are of interest in applications that include systems of Condensed Matter Physics, the Standard Model of Particle Physics, Lorentz-symmetry violating scenarios and Cosmology. In this work, we show how oscillons may be accommodated in a supersymmetric scenario. We adopt as our framework simple ($\mathcal{N}=1$) supersymmetry in $D=1+1$ dimensions. We focus on the bosonic sector with oscillon configurations and their (classi…
Using U_q(a_n^(1))- and U_q(a_2n^(2))-invariant R-matrices we construct exact S-matrices in two-dimensional space-time. These are conjectured to describe the scattering of solitons in affine Toda field theories. In order to find the spectrum of soliton bound states we examine the pole structure of these S-matrices in detail. We also construct the S-matrices for all scattering processes involving scalar bound states. In the last part of this paper we discuss the connection of these S-matrices with minimal N=1 and N=2 supersymmetric S-matrices. In particular we comment on the folding from N=2 to…
We discuss the supersymmetry algebra of the M theory fivebrane and obtain a new threebrane soliton preserving half of the six-dimensional supersymmetry. This solution is dimensionally reduced to various D-p-branes.
Fermionic modes of D-instanton wormholes from broken local supersymmetry
Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University（大阪公立大学）；College of Arts and Sciences, J. F. Oberlin University
We consider the fermionic bound states associated with a soliton-antisoliton pair in 1+1 dimensions which have zero energy when the solitons are infinitely far apart. We calculate the energies of these states when the solitons are separated by a finite distance. The energies decay exponentially with the distance between the soliton and antisoliton. When the fermion mass is much larger than the boson mass, the energy simplifies substantially. These energies may be interpreted as a contribution to the effective potential between the soliton and antisoliton. The character of this contribution dep…
Inspired by the tachyon-free non-supersymmetric heterotic SO(16)xSO(16) string we consider a special class of non-supersymmetric field theories: Those that can be obtained from supersymmetric field theories by supersymmetry breaking twists. We argue that such theories, like their supersymmetric counter parts, may still possess some fermionic symmetries as left-overs of the super gauge transformations and have special one-loop non-renormalization properties due to holomorphicity. In addition, we extend the supergraph techniques to these theories to calculate some explicit supersymmetry-breaking…
We consider the type-IIB supergravity vacua that include an internal $T^5$, depend on a single coordinate $r$ and respect a four-dimensional Poincaré symmetry, with the aim of highlighting low-energy spectra with broken supersymmetry and a bounded string coupling. These vacua are characterized by the flux $Φ$ of the self-dual five form in the internal torus, the length $\ell$ of the interval described by the coordinate $r$, a dilaton profile that is inevitably constant and a strictly positive dimensionless parameter $h$. As $\ell\rightarrow\infty$ while retaining finite values for $Φ$ and $\el…
In this paper we show how to quantize Hopf solitons using the Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if their Hopf charge is odd. Symmetries of classical minimal energy configurations induce loops in configuration space which give rise to constraints on the wave function. These constraints depend on whether the given loop is contractible. Our method is to exploit the relationship between the configuration spaces of the Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then use recent results in the Skyrme model to determine whether loops are…
(Replacement because mailer changed `hat' for supercript into something weird. The macro `\sp' has been used in place of the `hat' character in this revised version.) Fermionic Brownian paths are defined as paths in a space para\-metr\-ised by anticommuting variables. Stochastic calculus for these paths, in conjunction with classical Brownian paths, is described; Brownian paths on supermanifolds are developed and applied to establish a Feynman-Kac formula for the twisted Laplace-Beltrami operator on differential forms taking values in a vector bundle. This formula is used to give a proof of th…
We study some of the algebraic properties of the non-relativistic monopole. We find that we can construct theories that possess an exotic conserved fermionic charge that squares to the Casimir of the rotation group, yet do not possess an ordinary supersymmetry. This is in contrast to previous known examples with such exotic fermionic charges. We proceed to show that the presence of the exotic fermionic charge in the non-supersymmetric theory can nonetheless be understood using supersymmetric techniques, providing yet another example of the usefulness of supersymmetry in understanding non-super…
Considered are superparticle and superstring models invariant under supersymmetry in a target superspace and local extended worldsheet supersymmetry the latter replacing the fermionic $κ$--symmetry of the conventional Green--Schwarz formulations. (Talk given at the Conference on Geometry of Constrained Dynamical Systems, Cambridge, June 15-18, 1994).
We prove that the boundaries of all non-trivial 1+1 dimensional intrinsically fermionic symmetry-protected-topological phases, protected by finite on-site symmetries (unitary or anti-unitary), are supersymmetric quantum mechanical systems. This supersymmetry does not require any fine-tuning of the underlying Hamiltonian, arises entirely as a consequence of the boundary 't Hooft anomaly that classifies the phase and is related to a `Bose-Fermi' degeneracy different in nature from other well known degeneracies such as Kramers doublets.
Theories with axionic scalars admit three different Euclidean formulations, obtained by Wick rotation, Wick rotation combined with analytic continuation of the axionic scalars, and Wick rotation combined with Hodge dualization. We investigate the relation between these formulations for a class of theories which contains the sigma models of N=2 vector multiplets as a special case. It is shown that semi-classical amplitudes can be expressed equivalently using the two types of axionic actions, while the Hodge dualized version gives a different value for the instanton action unless the integration…
We couple two copies of the supersymmetric mKdV hierarchy by means of the algebraic dressing technique. This allows to deduce the whole set of $(N,N)$ supersymmetry transformations of the relativistic sector of the extended mKdV hierarchy and to interpret them as fermionic symmetry flows. The construction is based on an extended Riemann-Hilbert problem for affine Kac-Moody superalgebras with a half-integer gradation. A generalized set of relativistic-like fermionic local current identities is introduced and it is shown that the simplest one, corresponding to the lowest isospectral times $t_{\p…
The dynamics of a four dimensional generally covariant modified SU(N) Yang-Mills action, which depends on the complex structure of spacetime and not its metric, is studied. A general solution of the complex structure integrability conditions is found in the context of the G{2,2) Grassmannian manifold, which admits a global SL(4,C) symmetry group. A convenient definition of the physical energy and momentum permits the study of the vacuum and soliton sectors. The model has a set of conformally SU(2,2) invariant vacua and a set of Poincare invariant vacua. An algebraic integrability condition of …
We discuss several applications and extensions of our previous operator solution of the $N$-body Calogero problem, \ie N particles in 1 dimension subject to a two-body interaction of the form $\half \sum_{i,j}[ (x_i - x_j)^2 + g/ {(x_i - x_j)^2}]$. Using a complex representation of the deformed Heisenberg algebra underlying the Calogero model, we explicitly establish the equivalence between this system and anyons in the lowest Landau level. A construction based on supersymmetry is used to extend our operator method to include fermions, and we obtain an explicit solution of the supersymmetric C…
We study effects of backreaction of the fermionic modes localized by the baby Skyrmion in the (2+1)-dimensional Skyrme model. It is shown that there is a tower of fermionic modes of two different types, localized by the soliton, however there is only one fermionic level, which flows from positive to negative value as coupling increases. Considering the strong coupling regime we observe that the coupling of the bosonic field to the fermions may strongly deform the Skyrmion, in particular the regions of negative topological charge density appear.
We derive the Smarr formulae for two five-dimensional solutions of supergravity, which are asymptotically R^(1,3)xS^1; in particular, one has a magnetic bolt in its center, and one is a two-center solution. We show for both spacetimes that supersymmetry - and so the BPS-bound - is broken by the holonomy and how each topological feature of a space-like hypersurface enters Smarr's mass formula, with emphasis on the ones that give rise to the stated violation of the BPS-bound. In this light, we question if any violating extra-mass term in a spacetime with such asymptotics is only evident in the A…
A first-order `BPS' equation is obtained for 1/8 supersymmetric intersections of soliton-membranes (lumps) of supersymmetric (4+1)-dimensional massless sigma models, and a special non-singular solution is found that preserves 1/4 supersymmetry. For 4-dimensional hyper-Kähler target spaces ($HK_4$) the BPS equation is shown to be the low-energy limit of the equation for a Cayley-calibrated 4-surface in $\bE^4\times HK_4$. Similar first-order equations are found for stationary intersections of Q-lump-membranes of the massive sigma model, but now generic solutions preserve either 1/8 supersymmetr…
We consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized eta function a more systematic version of the derivative expansion for spectral assymmetry and that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in a multiflavour extension of the Goldstone-Wilczek model.We also propose an improved expansionof the heat kernelthat allows the tackling ofthe convergence issues and permits an automated computation of the coefficients
We consider the two most general families of the (1+1)D Dirac systems with transparent scalar potentials, and two related families of the paired reflectionless Schrodinger operators. The ordinary N=2 supersymmetry for such Schrodinger pairs is enlarged up to an exotic N=4 nonlinear centrally extended supersymmetric structure, which involves two bosonic integrals composed from the Lax-Novikov operators for the stationary Korteweg-de Vries hierarchy. Each associated single Dirac system displays a proper N=2 nonlinear supersymmetry with a non-standard grading operator. One of the two families of …
We construct a fermion system in a multi-kink-antikink soliton background, and present in an explicit form all its trapped configurations (bound state solutions) as well as scattering states. This is achieved by exploiting an exotic N=4 centrally extended nonlinear supersymmetry of completely isospectral pairs of reflectionless Schrodinger systems with potentials to be n-soliton solutions for the Korteweg-de Vries equation. The obtained reflectionless Dirac system with a position-dependent mass is shown to possess its own exotic nonlinear supersymmetry associated with the matrix Lax-Novikov op…
We derive the BPS equations satisfied by lump solitons in $(2+1)$-dimensional sigma models with toric 8-dimensional hyper-Kähler (${HK}_8$) target spaces and check they preserve 1/2 of the supersymmetry. We show how these solitons are realised in M theory as M2-branes wrapping holomorphic 2-cycles in the $\bE^{1,2}\times {HK}_8$ background. Using the $κ$-symmetry of a probe M2-brane in this background we determine the supersymmetry they preserve, and note that there is a discrepancy in the fraction of supersymmetry preserved by these solitons as viewed from the low energy effective sigma model…
We find supersymmetric extensions of the half-BPS soliton-impurity models in (1+1) dimensions which preserve half of the $\mathcal{N}=1$ supersymmetry. This is related to the fact that in the bosonic sector (i.e., the half-BPS soliton-impurity model), only one soliton (for example, the kink) is a BPS configuration which solves the pertinent Bogomolnyi equation and saturates the topological energy bound. On the other hand, the topological charge conjugate state (the antikink) is not a BPS solution. This means that it obeys the full Euler-Lagrange equation and does not saturate the topological e…
We examine the effect of one loop quantum corrections on the formation of nontopological solitons in a strongly coupled scalar-fermionic Yukawa theory. The exact one fermion loop contribution is incorporated by using a nonlocal method to correct the local derivative expansion approximation (DE) of the effective action. As the Yukawa coupling is increased we find that the nonlocal corrections play an increasingly important role. The corrections cause the scalar field to increase in depth while maintaining its size. This increases the energy of the bag configuration, but this is compensated for …
We construct the N=2, D=9 supergravity theory up to the quartic fermionic terms and derive the supersymmetry transformation rules for the fields modulo cubic fermions. We consider a class of p-brane solutions of this theory, the stainless p-branes, which cannot be isotropically oxidized into higher dimensions. The new stainless elementary membrane and elementary particle solutions are found. It is explicitly verified that these solutions preserve half of the supersymmetry.
We study the stability of supersymmetry breaking metastable vacua and supersymmetric vacua in the presence of solitons. The metastable vacua of supersymmetric QCD and those found elsewhere such as in models based on the SU(5) grand unified group support the existence of topological solitons. The vacua containing such topological defects can become unstable against decay into lower energy configurations. We show for a specific model that a finite region of the available parameter space of couplings becomes disallowed due to the presence of monopoles. In a manner similar to previous studies base…
We connect the quasinormal modes corresponding to Dirac fermions in various black holes backgrounds to an N=2 supersymmetric quantum mechanics algebra, which can be constructed from the radial part of the fermionic solutions of the Dirac equation. In the massless fermion case, the quasinormal modes are in bijective correspondence with the zero modes of the fermionic system and this results to unbroken supersymmetry. The massive case is more evolved but as we prove, supersymmetry remains unbroken even in this case.
We show how 1+1-dimensional fermionic symmetry-protected topological states (SPTs, i.e. nontrivial short-range entangled gapped phases of quantum matter whose boundary exhibits 't Hooft anomaly and whose bulk cannot be deformed into a trivial tensor product state under finite-depth local unitary transformations only in the presence of global symmetries), indeed can be unwound to a trivial state by enlarging the Hilbert space via adding extra degrees of freedom and suitably extending the global symmetries. The extended projective global symmetry on the boundary can become supersymmetric in a sp…
We consider the degeneracy between the Regge slope of mesons and baryons in QCD. We argue that within the "orientifold large-N approximation" asymptotically massive mesons and baryons become supersymmetric partners and hence degenerate. To this end, we generalize QCD by a SU(N) theory with a quark in the two-index antisymmetric representation. We show that in this framework the meson is represented by an oriented bosonic QCD-string and the baryon is represented by an un-oriented fermionic QCD-string. At large-N, due to an equivalence with super Yang-Mills, the tensions of the bosonic and the f…
We propose a lattice action for two dimensional super Yang-Mills theory with a twisted N=2 supersymmetry. The extended supersymmetry is fully and exactly realized on the lattice. The method employed is quite general and its extension to the N=4 supersymmetry in four dimensions is briefly presented. The lattice has a new type of ``fermionic'' links, where odd Grassmann variables, supercharges and fermionic connections sit. The Leibniz rule is preserved on the lattice, although in a modified ``shifted'' form that takes into account the link nature of both derivatives and supercharges. Superfield…
Fermionic domain-wall Skyrmions of QCD in a magnetic field
Department of Physics, Yamagata University（山形大学物理系）；Research and Education Center for Natural Sciences, Keio University（庆应义塾大学自然科学研究与教育中心）；Department of Physics, Keio University（庆应义塾大学物理系）
I discuss the role of spacetime supersymmetry in the interplay between strong/weak coupling duality and target space duality in string theory which arises in string/string duality. This can be seen via the construction of string soliton solutions which in $N=4$ compactifications of heterotic string theory break more than $1/2$ of the spacetime supersymmetries but whose analogs in $N=2$ and $N=1$ compactifications break precisely $1/2$ of the spacetime supersymmetries. As a result, these solutions may be interpreted as stable solitons in the latter two cases, and correspond to Bogomol'nyi-satur…
We discuss on the possible existence of a supersymmetric invariance in purely fermionic planar systems and its relation to the fermion-boson mapping in three-dimensional quantum field theory. We consider, as a very simple example, the bosonization of free massive fermions and show that, under certain conditions on the masses, this model displays a supersymmetric-like invariance in the low energy regime. We construct the purely fermionic expression for the supercurrent and the non-linear supersymmetry transformation laws. We argue that the supersymmetry is absent in the limit of massless fermio…
We study supersymmetric structure of the self-isospectral crystalline chains formed by N copies of the mutually displaced one-gap Lame systems. It is generated by the N(N-1) integrals of motion which are the first order matrix differential operators, by the same number of the nontrivial second order integrals, and by the N third order Lax integrals. We show that the structure admits distinct alternatives for a grading operator, and in dependence on its choice one of the third order matrix integrals plays either the role of the bosonic central charge or the role of the fermionic supercharge to …
An extended free fermionic construction of the internal N=1 world sheet supercurrent for four-dimensional superstring theory is given. We show how it can describe theories with massless fermions, and we discuss the corresponding N=2 superconformal algebra. As an intermediate step, we show that an internal N=2 global superconformal invariance occurs in any superstring theory with massless fermions at tree level. To demonstrate this fact, we give the N=2 supercurrents for a model with N=1 space-time supersymmetry and a model without space-time supersymmetry.
We holographically compute supercharge diffusion constants in supersymmetric field theories, dual to AdS black brane solutions of arbitrary dimension. This includes the extension of earlier work by Kontoudi and Policastro for D3-branes to M2- and M5-brane theories. We consider the case of vanishing chemical potential. In particular, we relate the product of a diffusion constant and the energy density to a universal result for the fermionic absorption cross section. This relation is analogous to the famous proof of universality of $η/ s$. We calculate the diffusion constants in two different wa…
We use a covariant phase space formalism to give a general prescription for defining Hamiltonian generators of bosonic and fermionic symmetries in diffeomorphism invariant theories, such as supergravities. A simple and general criterion is derived for a choice of boundary condition to lead to conserved generators of the symmetries on the phase space. In particular, this provides a criterion for the preservation of supersymmetries. For bosonic symmetries corresponding to diffeomorphisms, our prescription coincides with the method of Wald et al. We then illustrate these methods in the case of ce…
We derive a general relation between the bosonic and fermionic entanglement in the ground states of supersymmetric quadratic Hamiltonians. For this, we construct canonical identifications between bosonic and fermionic subsystems. Our derivation relies on a unified framework to describe both, bosonic and fermionic Gaussian states in terms of so-called linear complex structures $J$. The resulting dualities apply to the full entanglement spectrum between the bosonic and the fermionic systems, such that the von Neumann entropy and arbitrary Renyi entropies can be related. We illustrate our finding…
