Supersymmetric SU Research Articles

Fermion masses and mixing in SU(5)×D4 × U(1) model

We propose a supersymmetric SU(5)×Gf GUT model with flavor symmetry Gf=D4×U(1) providing a good description of fermion masses and mixing. The model has twenty eight free parameters, eighteen are fixed to produce approximative experimental values of the physical parameters in the quark and charged lepton sectors. In the neutrino sector, the TBM matrix is generated at leading order through type I seesaw mechanism, and the deviation from TBM studied to reconcile with the phenomenological values of the mixing angles. Other features in the charged sector such as Georgi–Jarlskog relations and CKM mixing matrix are also studied.

Likelihood analysis of supersymmetric SU(5) GUTs

We perform a likelihood analysis of the constraints from accelerator experiments and astrophysical observations on supersymmetric (SUSY) models with SU(5) boundary conditions on soft SUSY-breaking parameters at the GUT scale. The parameter space of the models studied has seven parameters: a universal gaugino mass m_{1/2}, distinct masses for the scalar partners of matter fermions in five- and ten-dimensional representations of SU(5), m_5 and m_{10}, and for the mathbf {5} and {bar{mathbf{5}}} Higgs representations m_{H_u} and m_{H_d}, a universal trilinear soft SUSY-breaking parameter A_0, and the ratio of Higgs vevs tan beta . In addition to previous constraints from direct sparticle searches, low-energy and flavour observables, we incorporate constraints based on preliminary results from 13 TeV LHC searches for jets + events and long-lived particles, as well as the latest PandaX-II and LUX searches for direct Dark Matter detection. In addition to previously identified mechanisms for bringing the supersymmetric relic density into the range allowed by cosmology, we identify a novel {tilde{u}_R}/{tilde{c}_R} - tilde{chi }^{0}_{1} coannihilation mechanism that appears in the supersymmetric SU(5) GUT model and discuss the role of {{tilde{nu }}_tau } coannihilation. We find complementarity between the prospects for direct Dark Matter detection and SUSY searches at the LHC.

The super-GUT CMSSM revisited

We revisit minimal supersymmetric SU(5) grand unification (GUT) models in which the soft supersymmetry-breaking parameters of the minimal supersymmetric Standard Model (MSSM) are universal at some input scale, $M_{in}$, above the supersymmetric gauge coupling unification scale, $M_{GUT}$. As in the constrained MSSM (CMSSM), we assume that the scalar masses and gaugino masses have common values, $m_0$ and $m_{1/2}$ respectively, at $M_{in}$, as do the trilinear soft supersymmetry-breaking parameters $A_0$. Going beyond previous studies of such a super-GUT CMSSM scenario, we explore the constraints imposed by the lower limit on the proton lifetime and the LHC measurement of the Higgs mass, $m_h$. We find regions of $m_0$, $m_{1/2}$, $A_0$ and the parameters of the SU(5) superpotential that are compatible with these and other phenomenological constraints such as the density of cold dark matter, which we assume to be provided by the lightest neutralino. Typically, these allowed regions appear for $m_0$ and $m_{1/2}$ in the multi-TeV region, for suitable values of the unknown SU(5) GUT-scale phases and superpotential couplings, and with the ratio of supersymmetric Higgs vacuum expectation values $\tan \beta \lesssim 6$.

Gauge interactions and topological phases of matter

We study the effects of strongly coupled gauge interactions on the properties of the topological phases of matter. In particular, we discuss fermionic systems with three spatial dimensions, protected by time-reversal symmetry. We first derive a sufficient condition for the introduction of a dynamical Yang–Mills field to preserve the topological phase of matter, and then show how the massless pions capture in the infrared the topological properties of the fermions in the ultraviolet. Finally, we use the S-duality of N=2 supersymmetric SU(2) gauge theory with Nf=4 flavors to show that the ν=16 phase of Majorana fermions can be continuously connected to the trivial ν=0 phase.

Non-perturbative quantum geometry III

The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stokes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stokes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.

The ground state of the D = 11 supermembrane and matrix models on compact regions

We establish a general framework for the analysis of boundary value problems of matrix models at zero energy on compact regions. We derive existence and uniqueness of ground state wavefunctions for the mass operator of the D=11 regularized supermembrane theory, that is the N=16 supersymmetric SU(N) matrix model, on balls of finite radius. Our results rely on the structure of the associated Dirichlet form and a factorization in terms of the supersymmetric charges. They also rely on the polynomial structure of the potential and various other supersymmetric properties of the system.

BPS pion domain walls in the supersymmetric chiral Lagrangian

We construct exact solutions of BPS pion domain walls in the four-dimensional $\mathcal{N}=1$ supersymmetric SU(N) chiral Lagrangian with pion masses introduced via linear and quadratic superpotentials. The model admits N discrete vacua in the center of SU(N) for the linear superpotential. In addition to the latter, new vacua appear for the quadratic superpotential. We find that the domain wall solutions of pions (Nambu-Goldstone bosons) that interpolate between a pair of (pion) vacua preserve half of supersymmetry. Contrary to our expectations, we have not been able to find domain walls involving the quasi-Nambu-Goldstone bosons present in the theory, which in turn has the consequence that not all vacua of the theory are connected by a BPS domain wall solution.

Threshold corrections to dimension-six proton decay operators in non-minimal SUSY SU(5) GUTs

We calculate the high and low scale threshold corrections to the D=6 proton decay mode in supersymmetric SU(5) grand unified theories with higher-dimensional representation Higgs multiplets. In particular, we focus on a missing-partner model in which the grand unified group is spontaneously broken by the 75-dimensional Higgs multiplet and the doublet–triplet splitting problem is solved. We find that in the missing-partner model the D=6 proton decay rate gets suppressed by about 60%, mainly due to the threshold effect at the GUT scale, while the SUSY-scale threshold corrections are found to be less prominent when sfermions are heavy.

SUSY SU(5)×S 4 GUT flavor model for fermion masses and mixings with adjoint, large θ 13 PMNS

We propose an $S_{4}$ flavor model based on supersymmetric (SUSY) SU(5) GUT. The first and third generations of \textbf{10} dimensional representations in SU(5) are all assigned to be $1_{1}$ of $S_{4}$. The second generation of \textbf{10} is to be $1_{2}$ of $S_{4}$. Right-handed neutrinos of singlet \textbf{1} and three generations of $\bar{\textbf{5}}$ are all assigned to be $3_{1}$ of $S_{4}$. The VEVs of two sets of flavon fields are allowed a moderate hierarchy, that is $\langle\Phi^{\nu}\rangle \sim \lambda_{c}\langle\Phi^{e}\rangle$. Tri-Bimaximal (TBM) mixing can be produced at both leading order (LO) and next to next to leading order (NNLO) in neutrino sector. All the masses of up-type quarks are obtained at LO. We also get the bottom-tau unification $m_{\tau}=m_{b}$ and the popular Georgi-Jarlskog relation $m_{\mu}=3m_{s}$ as well as a new mass relation $m_{e}=\frac{8}{27}m_{d}$ in which the novel Clebsch-Gordan (CG) factor arises from the adjoint field $H_{24}$. The GUT relation leads to a sizable mixing angle $\theta^{e}_{12} \sim \theta_{c}$ and the correct quark mixing matrix $V_{CKM}$ can also be realised in the model. The resulting CKM-like mixing matrix of charged leptons modifies the vanishing $\theta^{\nu}_{13}$ in TBM mixing to a large $\theta^{PMNS}_{13}\simeq\theta_{c}/\sqrt{2}$, in excellent agreement with experimental results. A Dirac CP violation phase $\phi_{12}\simeq\pm\pi/2$ is required to make the deviation from $\theta^{\nu}_{12}$ small. We also present some phenomenological numerical results predicted by the model.

Multifield dynamics of supersymmetric Higgs inflation inSU(5)GUT

We study the Higgs inflation model realized in the supersymmetric SU(5) grand unified theory (GUT), focusing on its multifield dynamics and prediction of cosmological observables. The requirement for GUT symmetry breaking during inflation imposes tight constraints on the model parameters. We find, nevertheless, with an appropriately chosen noncanonical Kahler potential the model is in excellent agreement with the present cosmological observation. The effects from multifield dynamics is found to be minor and thus, unlike other similar supersymmetric implementation of nonminimally coupled Higgs inflation, the prediction of this model is robust against multifield ambiguities.

The light bound states of supersymmetric SU(2) Yang-Mills theory

Supersymmetry provides a well-established theoretical framework for extensions of the standard model of particle physics and the general understanding of quantum field theories. We summarise here our investigations of N=1 supersymmetric Yang-Mills theory with SU(2) gauge symmetry using the non-perturbative first-principles method of numerical lattice simulations. The strong interactions of gluons and their superpartners, the gluinos, lead to confinement, and a spectrum of bound states including glueballs, mesons, and gluino-glueballs emerges at low energies. For unbroken supersymmetry these particles have to be arranged in supermultiplets of equal masses. In lattice simulations supersymmetry can only be recovered in the continuum limit since it is explicitly broken by the discretisation. We present the first continuum extrapolation of the mass spectrum of supersymmetric Yang-Mills theory. The results are consistent with the formation of supermultiplets and the absence of non-perturbative sources of supersymmetry breaking. Our investigations also indicate that numerical lattice simulations can be applied to non-trivial supersymmetric theories.

Resurrecting the minimal renormalizable supersymmetric SU(5) model

It is a well-known fact that the minimal renormalizable supersymmetric SU(5) model is ruled out assuming superpartner masses of the order of a few TeV. Giving up this constraint and assuming only SU(5) boundary conditions for the soft terms, we find that the model is still alive. The viable region of the parameter space typically features superpartner masses of order $10^2$ to $10^4$ TeV, with tan beta values between 2 and 5, but lighter spectra with single states around 10 TeV are also possible. The main constraints come from proton decay, the Higgs mass, the requirement of the SU(5) spectrum being reasonably below the Planck scale, and the lifetime of the universe. A generic feature of the model is metastability of the electroweak vacuum. In the absence of a suitable dark matter particle in the neutralino sector, a light (order GeV or smaller) gravitino is a natural candidate.

Partition function of N = 2 ∗ $$ \mathcal{N}={2}^{\ast } $$ SYM on a large four-sphere

We examine the partition function of N=2* supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N, is computed by saddle points lying on particular walls of marginal stability on the Coulomb branch of the theory on R^4. For N an even (odd) integer and \theta_YM=0, (\pi), these include a point of maximal degeneration of the Donagi-Witten curve to a torus where BPS dyons with electric charge [N/2] become massless. We argue that the dyon singularity is the lone saddle point in the SU(2) theory, while for SU(N) with N>2, we characterize potentially competing saddle points by obtaining the relations between the Seiberg-Witten periods at such points. Using Nekrasov's instanton partition function, we solve for the maximally degenerate saddle point and obtain its free energy as a function of g_YM and N, and show that the results are "large-N exact". In the large-N theory our results provide analytical expressions for the periods/eigenvalues at the maximally degenerate saddle point, precisely matching previously known formulae following from the correspondence between N=2* theory and the elliptic Calogero-Moser integrable model. The maximally singular point ceases to be a saddle point of the partition function above a critical value of the coupling, in agreement with the recent findings of Russo and Zarembo.

NLSP gluino and NLSP stop scenarios fromb−τYukawa unification

We present a study of b-tau Yukawa unified supersymmetric SU(4)_c x SU(2)_L x SU(2)_R model (with mu > 0), which predicts the existence of gluino - neutralino and stop - neutralino coannihilation scenarios compatible with the desired relic LSP neutralino dark matter abundance and other collider constraints. The NLSP gluino or NLSP stop masses vary between 400 GeV to ~ 1 TeV. The NLSP gluinos will be accessible at the 14 TeV LHC, while we hope that the NSLP stop solutions will be probed in future LHC searches. We also identify regions of the parameter space in which the gluino and the lighter stop are closely degenerate in mass, interchangeably playing the role of NLSP and NNLSP. We also update a previous study of t-b-tau Yukawa unification and show that NLSP gluino of mass ~ 1 TeV, with a mass difference between the gluino and neutralino of less than 80 GeV, can be realized consistent with the current collider and astrophysical constraints. We present benchmark points for b-tau and t-b-tau Yukawa unification that can be accessible at the LHC.

R-parity violation in SU(5)

We show that judiciously chosen R-parity violating terms in the minimal renormalizable supersymmetric SU(5) are able to correct all the phenomenologically wrong mass relations between down quarks and charged leptons. The model can accommodate neutrino masses as well. One of the most striking consequences is a large mixing between the electron and the Higgsino. We show that this can still be in accord with data in some regions of the parameter space and possibly falsified in future experiments.

Threshold corrections to baryon number violating operators in supersymmetric [formula omitted] GUTs

The nucleon decay is a significant phenomenon to verify grand unified theories (GUTs). For the precise prediction of the nucleon lifetime induced by the gauge bosons associated with the unified gauge group, it is important to include the renormalization effects on the Wilson coefficients of the dimension-six baryon number violating operators. In this study, we have derived the threshold corrections to these coefficients at the one-loop level in the minimal supersymmetric SU(5) GUT and the extended one with additional SU(5) vector-like pairs. As a result, it is found that the nucleon decay rate is suppressed about 5% in the minimal setup, and then the suppression could be O(10)% in the vector-like matter extensions.

Rigid holography and six-dimensional N = 2 0 $$ \mathcal{N}=\left(2,0\right) $$ theories on AdS5 × S $$ \mathbb{S} $$ 1

Field theories on anti-de Sitter (AdS) space can be studied by realizing them as low-energy limits of AdS vacua of string/M theory. In an appropriate limit, the field theories decouple from the rest of string/M theory. Since these vacua are dual to conformal field theories, this relates some of the observables of these field theories on AdS space to a subsector of the dual conformal field theories. We exemplify this ‘rigid holography’ by studying in detail the six-dimensional $$ \mathcal{N}=\left(2,0\right) $$ A K − 1 superconformal field theory (SCFT) on AdS5 × $$ \mathbb{S} $$ 1, with equal radii for AdS5 and for $$ \mathbb{S} $$ 1. We choose specific boundary conditions preserving sixteen supercharges that arise when this theory is embedded into Type IIB string theory on AdS5 × $$ \mathbb{S} $$ 5/ℤ K . On ℝ4,1 × $$ \mathbb{S} $$ 1, this six-dimensional theory has a 5(K − 1)-dimensional moduli space, with unbroken five-dimensional SU(K) gauge symmetry at (and only at) the origin. On AdS5 × $$ \mathbb{S} $$ 1, the theory has a 2(K − 1)-dimensional ‘moduli space’ of supersymmetric configurations. We argue that in this case the SU(K) gauge symmetry is unbroken everywhere in the ‘moduli space’ and that this five-dimensional gauge theory is coupled to a four-dimensional theory on the boundary of AdS5 whose coupling constants depend on the ‘moduli’. This involves non-standard boundary conditions for the gauge fields on AdS5. Near the origin of the ‘moduli space’, the theory on the boundary contains a weakly coupled four-dimensional $$ \mathcal{N}=2 $$ supersymmetric SU(K) gauge theory. We show that this implies large corrections to the metric on the ‘moduli space’. The embedding in string theory implies that the six-dimensional $$ \mathcal{N}=\left(2,0\right) $$ theory on AdS5 × $$ \mathbb{S} $$ 1 with sources on the boundary is a subsector of the large N limit of various four-dimensional $$ \mathcal{N}=2 $$ quiver SCFTs that remains non-trivial in the large N limit. The same subsector appears universally in many different four-dimensional $$ \mathcal{N}=2 $$ SCFTs. We also discuss a decoupling limit that leads to $$ \mathcal{N}=\left(2,0\right) $$ ‘little string theories’ on AdS5 × $$ \mathbb{S} $$ 1.

The role of field redefinition on renormalisability of a general [formula omitted] supersymmetric gauge theories

We investigate some issues on renormalisability of non-anticommutative supersymmetric gauge theory related to field redefinitions. We study one loop corrections to N=12 supersymmetric SU(N)×U(1) gauge theory coupled to chiral matter in component formalism, and show the procedure which has been introduced for renormalisation is problematic because some terms which are needed for the renormalisability of theory are missed from the Lagrangian. In order to prove the theory is renormalisable, we redefine the gaugino and the auxiliary fields (λ,F¯), which result in a modified form of the Lagrangian in the component formalism. Then, we show the modified Lagrangian has extra terms which are necessary for renormalisability of non-anticommutative supersymmetric gauge field theories. Finally, we prove N=12 supersymmetric gauge theory is renormalisable up to one loop corrections using standard method of renormalisation; besides, it is shown the effective action is gauge invariant.

Resurgence and the Nekrasov-Shatashvili limit: connecting weak and strong coupling in the Mathieu and Lamé systems

The Nekrasov-Shatashvili limit for the low-energy behavior of N=2 and N=2* supersymmetric SU(2) gauge theories is encoded in the spectrum of the Mathieu and Lam'e equations, respectively. This correspondence is usually expressed via an all-orders Bohr-Sommerfeld relation, but this neglects non-perturbative effects, the nature of which is very different in the electric, magnetic and dyonic regions. In the gauge theory dyonic region the spectral expansions are divergent, and indeed are not Borel-summable, so they are more properly described by resurgent trans-series in which perturbative and non-perturbative effects are deeply entwined. In the gauge theory electric region the spectral expansions are convergent, but nevertheless there are non-perturbative effects due to poles in the expansion coefficients, and which we associate with worldline instantons. This provides a concrete analog of a phenomenon found recently by Drukker, Marino and Putrov in the large N expansion of the ABJM matrix model, in which non-perturbative effects are related to complex space-time instantons. In this paper we study how these very different regimes arise from an exact WKB analysis, and join smoothly through the magnetic region. This approach also leads to a simple proof of a resurgence relation found recently by Dunne and Unsal, showing that for these spectral systems all non-perturbative effects are subtly encoded in perturbation theory, and identifies this with the Picard-Fuchs equation for the quantized elliptic curve.

IR dualities in general 3d supersymmetric SU(N) QCD theories

In the last twenty years, low-energy (IR) dualities have been found for many pairs of supersymmetric gauge theories with four supercharges, both in four space-time dimensions and in three space-time dimensions. In particular, duals have been found for 3d N=2 supersymmetric QCD theories with gauge group U(N), with F chiral multiplets in the fundamental representation, with F' chiral multiplets in the anti-fundamental representation, and with Chern-Simons level k, for all values of N, F, F' and k for which the theory preserves supersymmetry. For SU(N) theories the duals have been found in some cases, such as F=F' and F'=0, but not in the general case. In this note we find the IR dual for SU(N) SQCD theories with general values of N, F, F' and a non-zero k, which preserve supersymmetry.