Supersymmetric Point Research Articles

Eigenstate entanglement entropy in the integrable spin-1/2XYZ model.

We study the average and the standard deviation of the entanglement entropy of highly excited eigenstates of the integrable interacting spin-1/2XYZ chain away from and at special lines with U(1) symmetry and supersymmetry. We universally find that the average eigenstate entanglement entropy exhibits a volume-law coefficient that is smaller than that of quantum-chaotic interacting models. At the supersymmetric point, we resolve the effect that degeneracies have on the computed averages. We further find that the normalized standard deviation of the eigenstate entanglement entropy decays polynomially with increasing system size, which we contrast with the exponential decay in quantum-chaotic interacting models. Our results provide state-of-the art numerical evidence that integrability in spin-1/2 chains reduces the average and increases the standard deviation of the entanglement entropy of highly excited energy eigenstates when compared with those in quantum-chaotic interacting models.

Solving two-dimensional adjoint QCD with a basis-function approach

We apply a method (“eLCQ”) to find the asymptotic spectrum of a Hamiltonian from its symmetries to two-dimensional adjoint QCD. Streamlining the approach, we construct a complete set of asymptotic eigenfunctions in all parton sectors and use it in a basis-function approach to find the spectrum of the full theory. We are able to reproduce previous results including the degeneracy of fermionic and bosonic masses at the supersymmetric point, and to understand the properties of the lowest states in the massless theory. The approach taken here is continuous at fixed parton number, and therefore complementary to standard formulations, e.g. discretized light-cone quantization (DLCQ). Despite its limitation to rather small parton numbers, it can be used to test and validate conclusions of other frameworks in an independent way. Published by the American Physical Society 2024

Dualties of adjoint QCD3 from branes

We consider an ‘electric’ U(N) level k QCD3 theory with one adjoint Majorana fermion. Inspired by brane dynamics, we suggest that for k ≥ N/2 the massive m < 0 theory, in the vicinity of the supersymmetric point, admits a mathrm{U}{left(k-frac{N}{2}right)}_{-left(frac{1}{2}k+frac{3}{4}Nright),-left(k+frac{N}{2}right)} ‘magnetic’ dual with one adjoint Majorana fermion. The magnetic theory flows in the IR to a topological mathrm{U}{left(k-frac{N}{2}right)}_{-N,-left(k+frac{N}{2}right)} pure Chern-Simons theory in agreement with the dynamics of the electric theory. When k < N/2 the magnetic dual is mathrm{U}{left(frac{N}{2}-kright)}_{frac{1}{2}k+frac{3}{4}N,N} with one adjoint Majorana fermion. Depending on the sign of the fermion mass, the magnetic theory flows to either mathrm{U}{left(frac{N}{2}-kright)}_{N,N} or mathrm{U}{left(frac{N}{2}-kright)}_{frac{1}{2}N+k,N} TQFT. A second magnetic theory, mathrm{U}{left(N/2+kright)}_{frac{1}{2}k-frac{3}{4}N,N} , flows to either mathrm{U}{left(frac{N}{2}+kright)}_{-N,-N} or mathrm{U}{left(frac{N}{2}+kright)}_{-left(frac{1}{2}N-kright),-N} TQFT. Dualities for SO and USp theories with one adjoint fermion are also discussed.

Critical structure and emergent symmetry of Dirac fermion systems

Emergent symmetry in Dirac system means that the system acquires an enlargement of two basic symmetries at some special critical point. The continuous quantum criticality between the two symmetry broken phases can be described within the framework of Gross–Neveu–Yukawa (GNY) model. Using the first-order ε expansion in dimensions, we study the critical structure and emergent symmetry of the O(N)-GNY model with N f flavors of four-component Dirac fermions coupled strongly to an O(N) scalar field under a small O(N)-symmetry breaking perturbation. After determining the stable fixed point, we calculate the inverse correlation length exponent and the anomalous dimensions (bosonic and fermionic) for general N and N f . Further, we discuss the emergent-symmetry and the emergent supersymmetric critical point for on the basis of O(N)-GNY model. It turns out that the O(N)-GNY universality class is physically meaningful if and only if . On this premise, the small O(N)-symmetry breaking perturbation is always irrelevant in the O(N)-GNY universality class. Our studies show that the emergent symmetry in Dirac systems has an upper limit , depending on the flavor numbers N f . As a result, the emergent-O(4) and O(5) symmetries are possible to be found in Dirac systems with fermion flavor , and the emergent-O(4), O(5), O(6) and O(7) symmetries are expected to be found in the systems with fermion flavor . Our result suggests some richer transitions with emergent- symmetry, and so on. Interestingly, in the O(4)-GNY universality class, we find that there is a new supersymmetric critical point which is expected to be found in Dirac systems with fermion flavor .

Supersymmetry and multicriticality in a ladder of constrained fermions

Supersymmetric lattice models of constrained fermions are known to feature exotic phenomena such as superfrustration, with an extensive degeneracy of ground states, the nature of which is however generally unknown. Here we address this issue by considering a superfrustrated model, which we deform from the supersymetric point. By numerically studying its two-parameter phase diagram, we reveal a rich phenomenology. The vicinity of the supersymmetric point features period-4 and period-5 density waves which are connected by a floating phase (incommensurate Luttinger liquid) with smoothly varying density. The supersymmetric point emerges as a multicritical point between these three phases. Inside the period-4 phase we report a valence-bond solid type ground state that persists up to the supersymmetric point. Our numerical data for transitions out of density-wave phases are consistent with the Pokrovsky-Talapov universality class. Furthermore, our analysis unveiled a period-3 phase with a boundary determined by a competition between single and two-particle instabilities accompanied by a doubling of the wavevector of the density profiles along a line in the phase diagram.

Supersymmetric solitons and a degeneracy of solutions in AdS/CFT

We study Lorentzian supersymmetric configurations in D = 4 and D = 5 gauged mathcal{N} = 2 supergravity. We show that there are smooth 1/2 BPS solutions which are asymptotically AdS4 and AdS5 with a planar boundary, a compact spacelike direction and with a Wilson line on that circle. There are solitons where the S1 shrinks smoothly to zero in the interior, with a magnetic flux through the circle determined by the Wilson line, which are AdS analogues of the Melvin fluxtube. There is also a solution with a constant gauge field, which is pure AdS. Both solutions preserve half of the supersymmetries at a special value of the Wilson line. There is a phase transition between these two saddle-points as a function of the Wilson line precisely at the supersymmetric point. Thus, the supersymmetric solutions are degenerate, at least at the supergravity level. We extend this discussion to one of the Romans solutions in four dimensions when the Euclidean boundary is S1× Σg where Σg is a Riemann surface with genus g > 0. We speculate that the supersymmetric state of the CFT on the boundary is dual to a superposition of the two degenerate geometries.

Fermion-induced quantum critical point in the Landau-Devonshire model

Fluctuations can change the phase transition properties drastically. An example is the fermion-induced quantum critical point (FIQCP), in which fluctuations of the massless Dirac fermions turn a putative Landau-de Gennes first-order phase transition (FOPT) with a cubic boson interaction into a continuous one. However, for the Landau-Devonshire theory, which characterizes another very large class of FOPTs, its fate under the coupling with extra fluctuations has not been explored. Here, we discover a new type of FIQCP, in which the Dirac fermion fluctuations round the boson Landau-Devonshire FOPT into a continuous phase transition. By using the functional renormalization group analyses, we determine the condition for the appearance of this FIQCP. Moreover, we point out that the present FIQCP can be a supersymmetric critical point. We finally show that the low-temperature phase diagram can provide distinct experimental evidences to detect this FIQCP.

Machine Learning Gauged Supergravity

AbstractType IIB string theory on a 5‐sphere gives rise to gauged supergravity in five dimensions. Motivated by the fact that this is the context of the most widely studied example of the AdS/CFT correspondence, we undertake an investigation of its critical points. The scalar manifold is an coset, and the challenge is that it is 42‐dimensional. We take a Machine Learning approach to the problem using TensorFlow, and this results in a substantial increase in the number of known critical points. Our list of 32 critical points contains all five of the previously known ones, including an supersymmetric point identified by Khavaev, Pilch and Warner.

Supersymmetry for chiral symmetric quantum walks

Quantum walks have attracted attention as a promising platform realizing topological phenomena, and many physicists have introduced various types of indices to characterize topologically protected bound states that are robust against perturbations. In this paper, we introduce an index from a supersymmetric point of view. This allows us to define indices for all chiral symmetric quantum walks such as multi-dimensional split-step quantum walks and quantum walks on graphs, for which there has been no index theory. Moreover, the index gives a lower bound on the number of bound states robust against compact perturbations. We also calculate the index for several concrete examples including the unitary transformation that appears in Grover’s search algorithm.

SO(8) supergravity and the magic of machine learning

Using de Wit-Nicolai D = 4 mathcal{N} = 8 SO(8) supergravity as an example, we show how modern Machine Learning software libraries such as Google’s TensorFlow can be employed to greatly simplify the analysis of high-dimensional scalar sectors of some M-Theory compactifications. We provide detailed information on the location, symmetries, and particle spectra and charges of 192 critical points on the scalar manifold of SO(8) supergravity, including one newly discovered mathcal{N} = 1 vacuum with SO(3) residual symmetry, one new potentially stabilizable non-supersymmetric solution, and examples for “Galois conjugate pairs” of solutions, i.e. solution-pairs that share the same gauge group embedding into SO(8) and minimal polynomials for the cosmological constant. Where feasible, we give analytic expressions for solution coordinates and cosmological constants.As the authors’ aspiration is to present the discussion in a form that is accessible to both the Machine Learning and String Theory communities and allows adopting our methods towards the study of other models, we provide an introductory overview over the relevant Physics as well as Machine Learning concepts. This includes short pedagogical code examples. In particular, we show how to formulate a requirement for residual Supersymmetry as a Machine Learning loss function and effectively guide the numerical search towards supersymmetric critical points. Numerical investigations suggest that there are no further supersymmetric vacua beyond this newly discovered fifth solution.

4D $\mathcal{N}=1$ SYM supercurrent in terms of the gradient flow

The gradient flow and its small flow-time expansion provide a very versatile method to represent renormalized composite operators in a regularization-independent manner. This technique has been utilized to construct typical Noether currents such as the energy--momentum tensor and the axial-vector current in lattice gauge theory. In this paper, we apply the same technique to the supercurrent in the four-dimensional $\mathcal{N}=1$ super Yang--Mills theory (4D $\mathcal{N}=1$ SYM) in the Wess--Zumino gauge. Since this approach provides a priori a representation of the properly normalized conserved supercurrent, our result should be useful, e.g., in lattice numerical simulations of the 4D $\mathcal{N}=1$ SYM; the conservation of the so-constructed supercurrent can be used as a criterion for the supersymmetric point toward which the gluino mass is tuned.

Quench dynamics in two-dimensional integrable SUSY models

.We analyse quench processes in two-dimensional quantum field theories with an infinite number of conservation laws which also include fermionic charges that close a N = 1 supersymmetric algebra. While in general the quench protocol induces a breaking of supersymmetry, we show that there are particular initial states which also ensure the persistence of supersymmetry for the dynamics out of equilibrium. We discuss the conditions that identify such states and, as application, we present the significant cases of the Tricritical Ising model and the Sine–Gordon model at its supersymmetric point. We also address the issue of the generalised Gibbs ensemble in the presence of fermionic conserved charges.

SUSY see-saw and NMSO(10)GUT inflation after BICEP2

Supersymmetric see-saw slow roll inflection point inflation occurs along a MSSM D-flat direction associated with gauge invariant combination of Higgs, slepton and right-handed sneutrino at a scale set by the right-handed neutrino mass $M_{{\nu }^{c}} \sim 10^{6}\!\,-\,\!10^{13}$ GeV. The tensor to scalar perturbation ratio r∼10−3 can be achieved in this scenario. However, this scenario faced difficulty in being embedded in the realistic new minimal supersymmetric SO(10) grand unified theory (NMSO(10)GUT). The recent discovery of B-mode polarization by BICEP2, changes the prospects of NMSO(10)GUT inflation. Inflection point models become strongly disfavoured, as the trilinear coupling of SUSY see-saw inflation potential gets suppressed relative to the mass parameter favoured by BICEP2. Large values of r≈0.2 can be achieved with super-Planck scale inflaton values and mass scales of inflaton ≥10 13 GeV. In NMSO(10)GUT, this can be made possible with an admixture of heavy Higgs doublet fields, i.e., other than MSSM Higgs field, which are present and have masses of order GUT scale.

Simulation of supersymmetric quantum mechanics in a Cooper-pair box shunted by a Josephson rhombus

Supersymmetries in quantum mechanics offer a way to obtain degeneracies in the excitation spectrum which do not originate from selection rules. The mechanism behind the degeneracies is the same as the one that leads to the miraculous cancellations of divergences in supersymmetric field theories found in the high energy physics context. Even though of importance, there is up to now no realistic proposal of non-integrable systems that show level degeneracies due to a supersymmetric structure. Here, we propose an implementation of a quantum-mechanical supersymmetry in a Cooper-pair box shunted by a Josephson junction rhombus which is effectively $\pi$-periodic in the superconducting phase difference. For a characteristic ratio between the strength of the $2\pi$- and the $\pi$-periodic junction, we find a two-fold degeneracy of all the energy levels all the way from the weak junction/charge qubit limit to the strong junction/transmon regime. We provide explicit values for the parameters of the rhombus and show that tuning in and out of the supersymmetric point is easily achieved by varying an external gate voltage. We furthermore discuss a microwave experiment to detect the supersymmetry and conclude that it could indeed be simulated with currently existing Josephson junction technology.

Emergent Supersymmetry from Strongly Interacting Majorana Zero Modes.

We show that a strongly interacting chain of Majorana zero modes exhibits a supersymmetric quantum critical point corresponding to the c=7/10 tricritical Ising model, which separates a critical phase in the Ising universality class from a supersymmetric massive phase. We verify our predictions with numerical density-matrix-renormalization-group computations and determine the consequences for tunneling experiments.

Universal dS vacua in STU-models

Stable de Sitter solutions in minimal F-term supergravity are known to lie close to Minkowski critical points. We consider a class of STU-models arising from type IIB compactifications with generalised fluxes. There, we apply an analytical method for solving the equations of motion for the moduli fields based on the idea of treating derivatives of the superpotential of different orders up to third as independent objects. In particular, supersymmetric and no-scale Minkowski solutions are singled out by physical reasons. Focusing on the study of dS vacua close to supersymmetric Minkowski points, we are able to elaborate a complete analytical treatment of the mass matrix based on the sGoldstino bound. This leads to a class of interesting universal dS vacua. We finally explore a similar possibility around no-scale Minkowski points and discuss some examples.

Cluster Luttinger liquids and emergent supersymmetric conformal critical points in the one-dimensional soft-shoulder Hubbard model

We investigate the quantum phases of hard-core bosonic atoms in an extended Hubbard model where particles interact via soft-shoulder potentials in one dimension. Using a combination of field-theoretical methods and strong-coupling perturbation theory, we demonstrate that the low-energy phase can be a conformal cluster Luttinger liquid (CLL) phase with central charge $c=1$, where the microscopic degrees of freedom correspond to mesoscopic ensembles of particles. Using numerical density-matrix renormalization-group methods, we demonstrate that the CLL phase [first predicted in M. Mattioli et al., Phys. Rev. Lett. 111, 165302 (2013)] is separated from a conventional Tomonaga-Luttinger liquid by an exotic critical point with central charge $c=\frac{3}{2}$. The latter is expression of an emergent conformal supersymmetry, which is not present in the original Hamiltonian. We discuss the observability of the CLL phase in realistic experimental settings with weakly dressed Rydberg atoms confined to optical lattices. Using quantum Monte Carlo simulations, we show that the typical features of CLLs are stable up to comparatively high temperatures. Using exact diagonalizations and quantum trajectory methods, we provide a protocol for adiabatic state preparation as well as quantitative estimates on the effects of particle losses.

Investigation of neutralino pair production in photon-photon collider at the ILC

Neutralino pair production via photon-photon collision is analyzed in the context of the minimal supersymmetric standard model at a future linear collider. Since the photon does not have self- coupling, this process is only possible at next-to-leading order (NLO), and all the possible diagrams are calculated for the photon-photon interaction, including box, triangle, and quartic coupling diagrams. Numerical analysis of the production rates for ${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}$, ${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{1}^{0}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{2}^{0}$ and ${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{2}^{0}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{2}^{0}$ are presented for four new distinct benchmark models which are presented in the light of LHC8. Angular dependence of each neutralino pair for the benchmark points is also analyzed. Total integrated photonic cross section goes up to 1.43 fb for the ${\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{2}^{0}{\stackrel{\texttildelow{}}{\ensuremath{\chi}}}_{2}^{0}$ pairs at $\sqrt{s}=1\text{ }\text{ }\mathrm{TeV}$ for the radiatively driven natural supersymmetric benchmark point.

RG flows in 6D N = (1,0) SCFT from SO(4) half-maximal 7D gauged supergravity

We study $N=2$ seven-dimensional gauged supergravity coupled to three vector multiplets with $SO(4)$ gauge group. The resulting gauged supergravity contains 10 scalars consisting of the dilaton and 9 vector multiplet scalars parametrized by $SO(3,3)/SO(3)\times SO(3)$ coset manifold. The maximally supersymmetric $AdS_7$ vacuum with unbroken $SO(4)$ symmetry is identified with a $(1,0)$ SCFT in six dimensions. We find one new supersymmetric $AdS_7$ critical point preserving $SO(3)_{\textrm{diag}}\subset SO(3)\times SO(3)\sim SO(4)$ and study a holographic RG flow interpolating between the $SO(4)$ and the new $SO(3)$ supersymmetric critical points. The RG flow is driven by a vacuum expectation value of a dimension-four operator and describes a deformation of the UV $(1,0)$ SCFT to another supersymmetric fixed point in the IR. In addition, a number of non-supersymmetric critical points are identified, and some of them are stable with all scalar masses above the BF bound. RG flows to non-conformal $N=(1,0)$ Super Yang-Mills with $SO(2)\times SO(2)$ and $SO(2)$ symmetries are also investigated. Some of these flows have physically acceptable IR singularities since the scalar potential is bounded above. These provide physical RG flows from $(1,0)$ SCFT to non-conformal field theories in six dimensions.

Deformations of large N = (4, 4) 2D SCFT from 3D gauged supergravity

Supersymmetric and non-supersymmetric deformations of large $N=(4,4)$ SCFT with superconformal symmetry $D^1(2,1;\alpha)\times D^1(2,1;\alpha)$ are explored in the gravity dual described by a Chern-Simons $N=8$, $(SO(4)\times SO(4))\ltimes \mathbf{T}^{12}$ gauged supergravity in three dimensions. For $\alpha>0$, the gauged supergravity describes an effective theory of the maximal supergravity in nine dimensions on $AdS_3\times S^3\times S^3$ with the parameter $\alpha$ being the ratio of the two $S^3$ radii. We consider the scalar manifold of the supergravity theory of the form $SO(8,8)/SO(8)\times SO(8)$ and find a number of stable non-supersymmetric $AdS_3$ critical points for some values of $\alpha$. These correspond to non-supersymmetric IR fixed points of the UV $N=(4,4)$ SCFT dual to the maximally supersymmetric critical point. We study the associated RG flow solutions interpolating between these fixed points and the UV $N=(4,4)$ SCFT. Possible supersymmetric flows to non-conformal field theories are also investigated. Additionally, a half-supersymmetric domain wall within this gauged supergravity is obtained.