Supersymmetric Case Research Articles

Magnetic discrete gauge field in the confining vacua and the supersymmetric index

It has recently been argued that the confining vacua of Yang-Mills theory in the far infrared can have topological degrees of freedom given by magnetic $\mathbb{Z}_q$ gauge field, both in the non-supersymmetric case and in the N=1 supersymmetric case. In this short note we give another piece of evidence by computing and matching the supersymmetric index of the pure super Yang-Mills theory both in the ultraviolet and in the infrared.

Compatible abelian symmetries in N-Higgs-doublet models

We analyze the compatibility between abelian symmetries acting in two different sectors of a theory using the Smith Normal Form method. We focus on N-Higgs-doublet models (NHDMs) and on the compatibility between symmetries in the Higgs potential and in the Yukawa interactions, which were separately analyzed previous works. It is shown that two equal (isomorphic) symmetry groups that act in two separate sectors are not necessarily compatible in the whole theory and an upper bound is found for the size of the group that can be implemented in the entire NHDM. We also develop useful techniques to analyze compatibility and extend a symmetry from one sector to another. Consequences to the supersymmetric case are briefly discussed.

R2 inflation from scale invariant supergravity and anomaly free superstrings with fluxes

The scale invariant gravity theory coupled to conformally invariant matter is investigated. We show that in the non-supersymmetric case the conformally coupled scalars belong to an manifold, while in the supersymmetric case the scalar manifold becomes isomorphic to the Kählerian space =. In both cases when the underlying scale symmetry is preserved the vacuum corresponds to de Sitter space. Once the scale symmetry is broken by quantum effects, a transition to flat space becomes possible. We argue that the scale violating terms are induced by anomalies related to a symmetry. The anomaly is resolved via the gauging of a Peccei-Quinn axion shift symmetry. The theory describes an inflationary transition from de Sitter to flat Minkowski space, very similar to the Starobinsky inflationary model. The extension to metastable de Sitter superstring vacua is also investigated. The scalar manifold is extended to a much richer manifold, but it contains always as a sub-manifold. In superstrings the metastability is induced by axions that cure the anomalies in chiral (or even ) supersymmetric vacua via a Green-Schwarz/Peccei-Quinn mechanism generalized to four dimensions. We present some typical superstring models and discuss the possible stabilization of the no-scale modulus.

Loop corrections to soft theorems in gauge theories and gravity

In this paper, we study loop corrections to the recently proposed new soft theorem of Cachazo-Strominger, for both gravity and gauge theory amplitudes. We first review the proof of its tree-level validity based on BCFW recursion relations, which also establishes an infinite series of universals soft functions for MHV amplitudes, and a generalization to supersymmetric cases. For loop corrections, we focus on infrared finite, rational amplitudes at one loop, and apply recursion relations with boundary or double-pole contributions. For all-plus amplitudes, we prove that the subleading soft-theorems are exact to all multiplicities for both gauge and gravity amplitudes. For single-minus amplitudes, while the subleading soft-theorems are again exact for the minus-helicity soft leg, for plus-helicity loop corrections are required. Using recursion relations, we identify the source of such mismatch as stemming from the special contribution containing double poles, and obtain the all-multiplicity one-loop corrections to the subleading soft behavior in Yang-Mills theory. We also comment on the derivation of soft theorems using BCFW recursion in arbitrary dimensions.

Non-supersymmetric, multi-center solutions with topological flux

We find an infinite class of non-supersymmetric multi-center solutions to the STU model in five-dimensional ungauged supergravity coupled to two vector multiplets. The solutions are obtained by solving a system of linear equations on a class of Ricci-scalar-flat K\"ahler manifolds studied by LeBrun. After imposing an additional U(1) isometry in the base, we solve the axisymmetric $SU(\infty)$ Toda equation and obtain explicit supergravity solutions containing arbitrary numbers of 2-cycles with cohomological fluxes of all three flavors. This improves upon a previous result where only two of the three fluxes were topologically non-trivial. Imposing regularity and absence of closed timelike curves, we obtain "bubble equations" highly reminiscent of those known in the supersymmetric case. Thus we extend much of the analysis done for BPS bubbling solutions to this new family of non-supersymmetric bubbling solutions.

Searching for Fermi surfaces in super-QED

The exploration of strongly-interacting finite-density states of matter has been a major recent application of gauge-gravity duality. When the theories involved have a known Lagrangian description, they are typically deformations of large $N$ supersymmetric gauge theories, which are unusual from a condensed-matter point of view. In order to better interpret the strong-coupling results from holography, an understanding of the weak-coupling behavior of such gauge theories would be useful for comparison. We take a first step in this direction by studying several simple supersymmetric and non-supersymmetric toy model gauge theories at zero temperature. Our supersymmetric examples are $\mathcal{N}=1$ super-QED and $\mathcal{N}=2$ super-QED, with finite densities of electron number and R-charge respectively. Despite the fact that fermionic fields couple to the chemical potentials we introduce, the structure of the interaction terms is such that in both of the supersymmetric cases the fermions do not develop a Fermi surface. One might suspect that all of the charge in such theories would be stored in the scalar condensates, but we show that this is not necessarily the case by giving an example of a theory without a Fermi surface where the fermions still manage to contribute to the charge density.

7 keV sterile neutrino dark matter from split flavor mechanism

The recently discovered X-ray line at about 3.5 keV can be explained by sterile neutrino dark matter with mass, ms≃7 keV, and the mixing, sin22θ∼10−10. Such sterile neutrino is more long-lived than estimated based on the seesaw formula, which strongly suggests an extra flavor structure in the seesaw sector. We show that one can explain both the small mass and the longevity based on the split flavor mechanism where the breaking of flavor symmetry is tied to the breaking of the B−L symmetry. In a supersymmetric case we find that the 7 keV sterile neutrino implies the gravitino mass about 100 TeV.

Cogenesis in a universe with vanishing [formula omitted] within a gauged [formula omitted] extension

We consider a gauged U(1)x extension of the standard model and of the minimal supersymmetric standard model where the dark matter fields are charged under U(1)x and carry lepton number while the standard model fields and fields of the minimal supersymmetric standard model are neutral under U(1)x. We consider leptogenesis in this class of models with all fundamental interactions having no violation of lepton number, and the total B–L in the universe vanishes. Such leptogenesis leads to equal and opposite lepton numbers in the visible sector and in the dark sector, and thus also produces asymmetric dark matter. Part of the lepton number generated in the leptonic sector subsequently transfer to the baryonic sector via sphaleron interactions. The stability of the dark particles is protected by the U(1)x gauge symmetry. A kinetic mixing between the U(1)x and the U(1)Y gauge bosons allows for dissipation of the symmetric component of dark matter. The case when U(1)x is U(1)B–L is also discussed for the supersymmetric case. This case is particularly interesting in that we have a gauged U(1)B–L which ensures the conservation of B–L with an initial condition of a vanishing B–L in the universe. Phenomenological implications of the proposed extensions are discussed, which includes implications for electroweak physics, neutrino masses and mixings, and lepton flavor changing processes such as ℓi→ℓjγ. We also briefly discuss the direct detection of the dark matter in the model.

Super-Whittaker vector at c = 3/2

The degenerate Whittaker vector of the superconformal algebra can be represented in terms of Jack superpolynomials. However, in this representation the norm of the Whittaker vector involves a scalar product with respect to which the Jack superpolynomials are not orthogonal. In this note, we point out that this defect can be cured at c = 3/2 by means of a trick specific to the supersymmetric case. At c = 3/2, we thus end up with a closed-form expression for the norm of the degenerate super-Whittaker vector. Granting the super-version of the AGT conjecture, this closed-form expression should be equal to the -symmetric SU(2) pure-gauge instanton partition function—the corresponding equality taking the form of a rather nontrivial combinatorial identity.

Volume Independence in the LargeNLimit and an Emergent Fermionic Symmetry

Large-N volume independence in circle-compactified QCD with adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories is believed to possess a Hagedorn density of hadronic states. It turns out that these properties are in apparent tension with each other, because a Hagedorn density of states typically implies a phase transition at some finite radius. This tension is resolved if there are degeneracies between the spectra of bosonic and fermionic states, as happens in the N(f) = 1 supersymmetric case. Resolution of the tension for N(f) >1 then suggests the emergence of a fermionic symmetry at large N, where there is no supersymmetry. We can escape the Coleman-Mandula theorem since the N = ∞ theory is free, with a trivial S matrix. We show an example of such a spectral degeneracy in a nonsupersymmetric toy example which has a Hagedorn spectrum.

Modular Invariance for Twisted Modules over a Vertex Operator Superalgebra

The purpose of this paper is to generalize Zhu’s theorem about characters of modules over a vertex operator algebra graded by integer conformal weights, to the setting of a vertex operator superalgebra graded by rational conformal weights. To recover $${SL_2(\mathbb{Z})}$$ -invariance of the characters it turns out to be necessary to consider twisted modules alongside ordinary ones. It also turns out to be necessary, in describing the space of conformal blocks in the supersymmetric case, to include certain ‘odd traces’ on modules alongside traces and supertraces. We prove that the set of supertrace functions, thus supplemented, spans a finite dimensional $${SL_2(\mathbb{Z})}$$ -invariant space. We close the paper with several examples.

Supersymmetric M5 brane theories on R × CP2

We propose 4 and 12 supersymmetric conformal Yang-Mills-Chern-Simons theories on R × CP2 as multiple representations of the theory on M5 branes. These theories are obtained by twisted Zk modding and dimensional reduction of the 6d (2,0) superconformal field theory on R × S5 and have a discrete coupling constant $ \frac{1}{{g_{{Y\;M}}^2}}=\frac{k}{{4{\pi^2}}} $ with natural number k. Instantons in these theories are expected to represent the Kaluza-Klein modes. For the k = 1, 2 cases, we argue that the number of supersymmetries in our theories should be enhanced to 32 and 16, respectively. For the k = 3 case, only the 4 supersymmetric theory gets the supersymmetric enhancement to 8. For the 4 supersymmetric case, the vacuum structure becomes more complicated as there are degenerate supersymmetric vacua characterized by fuzzy spheres. We calculate the perturbative part of the SU(N ) gauge group Euclidean path integral for the index function at the symmetric phase of the 4 supersymmetric case and confirm it with the known half-BPS index. From the similar twisted Z k modding of the AdS7 × S4 geometry, we speculate that the M region is for k ≲ N 1/3 and the type IIA region is N 1/3 ≲ k ≲ N. When nonperturbative corrections are included, our theories are expected to produce the full index of the 6d (2,0) theory.

The Freudenthal gauge symmetry of the black holes of N = 2, d = 4 supergravity

We show that the representation of black-hole solutions in terms of the variables H M which are harmonic functions in the supersymmetric case is non-unique due to the existence of a local symmetry in the effective action. This symmetry is a continuous (and local) generalization of the discrete Freudenthal transformations initially introduced for the black-hole charges and can be used to rewrite the physical fields of a solution in terms of entirely different-looking functions.

Nonextremal black holes in gauged supergravity and the real formulation of special geometry II

In Klemm and Vaughan (2012 arXiv:1207.2679), a new prescription for finding nonextremal black hole solutions to , D = 4 Fayet–Iliopoulos gauged supergravity was presented, and explicit solutions of various models containing one vector multiplet were constructed. Here, we use the same method to find new nonextremal black holes to more complicated models. We also provide a general recipe to construct non-BPS extremal solutions for an arbitrary prepotential, as long as an axion-free condition holds. These follow from a set of first-order conditions, and are related to the corresponding supersymmetric black holes by a multiplication of the charge vector with a constant field rotation matrix S. The fake superpotential driving this first-order flow is nothing else than Hamilton’s characteristic function in a Hamilton–Jacobi formalism, and coincides in the supersymmetric case (when S is plus or minus the identity) with the superpotential proposed by Dall’Agata and Gnecchi (2011 J. High Energy Phys.JHEP03(2011)037). For the nonextremal black holes that asymptote to (magnetic) AdS, we compute both the mass coming from holographic renormalization and the one appearing in the superalgebra. The latter correctly vanishes in the BPS case, but also for certain values of the parameters that do not correspond to any known supersymmetric solution of gauged supergravity. We finally show that the product of all horizon areas depends only on the charges and the asymptotic value of the cosmological constant.

Accidental SUSY: enhanced bulk supersymmetry from brane back-reaction

We compute how bulk loops renormalize both bulk and brane effective interactions for codimension-two branes in 6D gauged chiral supergravity, as functions of the brane tension and brane-localized flux. We do so by explicitly integrating out hyper- and gauge-multiplets in 6D gauged chiral supergravity compactified to 4D on a flux-stabilized 2D rugby-ball geometry, specializing the results of a companion paper, arXiv:1210.3753, to the supersymmetric case. While the brane back-reaction generically breaks supersymmetry, we show that the bulk supersymmetry can be preserved if the amount of brane-localized flux is related in a specific BPS-like way to the brane tension, and verify that the loop corrections to the brane curvature vanish in this special case. In these systems it is the brane-bulk couplings that fix the size of the extra dimensions, and we show that in some circumstances the bulk geometry dynamically adjusts to ensure the supersymmetric BPS-like condition is automatically satisfied. We investigate the robustness of this residual supersymmetry to loops of non-supersymmetric matter on the branes, and show that supersymmetry-breaking effects can enter only through effective brane-bulk interactions involving at least two derivatives. We comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.

Induced boundary flow on the c = 1 orbifold moduli space

Boundary flow in the c = 1 2d CFT of a orbifold of a free boson on a circle is considered. Adding a bulk marginal operator to the c = 1 orbifold branch induces a boundary flow. We show that this flow is consistent for any bulk marginal operator and known initial given boundary condition. The supersymmetric case is also mentioned. For the circle branch of the moduli space, this has been shown by Fredenhagen et al (2007 J. Phys. A: Math. Theor. 40 F17). The ground state multiplicity (gb) is calculated and it is shown that it does indeed decrease.

Supersymmetry and mass gap in2+1dimensions: A gauge invariant Hamiltonian analysis

A Hamiltonian formulation of Yang-Mills-Chern-Simons theories with $0\leq N\leq 4$ supersymmetry in terms of gauge-invariant variables is presented, generalizing earlier work on nonsupersymmetric gauge theories. Special attention is paid to the volume measure of integration (over the gauge orbit space of the fields) which occurs in the inner product for the wave functions and arguments relating it to the renormalization of the Chern-Simons level number and to mass-gaps in the spectrum of the Hamiltonians are presented. The expression for the integration measure is consistent with the absence of mass gap for theories with extended supersymmetry (in the absence of additional matter hypermultiplets and/or Chern-Simons couplings), while for the minimally supersymmetric case, there is a mass-gap, the scale of which is set by a renormalized level number, in agreement with indications from existing literature. The realization of the supersymmetry algebra and the Hamiltonian in terms of the gauge invariant variables is also presented.

Holographic glueballs and infrared wall driven by dilaton

We study glueballs in the holographic gauge theories, supersymmetric and non-super symmetric cases, which are given by the type IIB superstring solutions with non-trivial dilaton. In both cases, the dilaton reflects the condensate of the gauge field strength, $<F^2>$, which is responsible to the linear confining potential between the quark and anti-quark. Then we could see the meson spectra. On the other hand, the glueball spectra are not found in the supersymmetric case. We need a sharp wall, which corresponds to an infrared cutoff, in order to obtain the glueballs. In the non-supersymmetric case, the quantized glueballs are actually observed due to the existence of such a wall driven by the dilaton. The strings and D-branes introduced as building blocks of hadrons are pushed out by this wall, and we could see the Regge behavior of the higher spin meson and glueball states. We find that the slope of the glueball trajectory is half of the flavor meson's one. As for the low spin glueballs, they are studied by solving the fluctuations of the bulk fields, and their discrete spectra are shown.

Vortex-type solutions in ABJM theory

We review our recent investigations on vortex type-solutions in ABJM theory without and with mass deformation. By imposing suitable supersymmetric conditions, we obtain vortex-type half-BPS equations and also its energy bound. For the undeformed ABJM theory, the resulting half-BPS equation is the same as that in SYM theory. For the mass-deformed ABJM theory, the half-BPS equations for U(2)×U(2) case reduce to the vortex equation in Maxwell-Higgs theory, which supports static regular multi-vortex solutions. In U(N)×U(N) case with N > 2 we obtain the nonabelian vortex equation of Yang-Mills-Higgs theory with a suitable ansatz. We also discuss less supersymmetric cases.

Aspects of symmetry breaking in SO(10) GUTs

I review some recent results on the Higgs sector of minimal SO(10) grand unified theories both with and without supersymmetry. It is shown that nonsupersymmetric SO(10) with just one adjoint triggering the first stage of the symmetry breaking does provide a successful gauge unification when radiative corrections are taken into account in the scalar potential, while in the supersymmetric case it is argued that the troubles in achieving a phenomenologically viable breaking with representations up to the adjoint are overcome by considering the flipped SO(10) embedding of the hypercharge.