Supersymmetric Quantum Chromodynamics Research Articles

Perturbative calculation of supersymmetric gradient flow in 𝒩 = 1 supersymmetric QCD

Abstract We demonstrate perturbative calculations of supersymmetric gradient flow in four-dimensional ${\mathcal {N}=1}$ supersymmetric quantum chromodynamics (SQCD). A remarkable property of the gradient flow is to make ultraviolet (UV) divergences of flowed field correlators milder. To illustrate this property, we calculate two-point functions for the flowed fields in SQCD at the one-loop level and investigate their UV divergence structure. After renormalizing the SQCD at the boundary, the two-point functions of flowed gauge supermultiplets are shown to be UV-finite. On the other hand, those for flowed matter supermultiplets require extra wave function renormalization, which are found to be the common factor for all the fields in the multiplets.

An alternative to the Teukolsky equation

We conjecture a new ordinary differential equation exactly isospectral to the radial component of the homogeneous Teukolsky equation. We find this novel relation by a hidden symmetry implied from a four-dimensional $\mathcal{N}=2$ supersymmetric quantum chromodynamics. Our proposal is powerful both in analytical and in numerical studies. As an application, we derive high-order perturbative series of quasinormal mode frequencies in the slowly rotating limit. We also test our result numerically by comparing it with a known technique.

Full-Color Two-Loop Four-Gluon Amplitude in N=2 Supersymmetric QCD.

We present the fully integrated form of the two-loop four-gluon amplitude in N=2 supersymmetric quantum chromodynamics with gauge group SU(N_{c}) and with N_{f} massless supersymmetric quarks (hypermultiplets) in the fundamental representation. Our result maintains full dependence on N_{c} and N_{f}, and relies on the existence of a compact integrand representation that exhibits the duality between color and kinematics. Specializing to the N=2 superconformal theory, where N_{f}=2N_{c}, we obtain remarkably simple amplitudes that have an analytic structure close to that of N=4 super-Yang-Mills theory, except that now certain lower-weight terms appear. We comment on the corresponding results for other gauge groups.

Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking

We discuss consequences of the ’t Hooft anomaly matching condition for Quantum Chromodynamics (QCD) with massless fundamental quarks. We derive the new discrete ’t Hooft anomaly of massless QCD for generic numbers of color Nc and flavor Nf , and an exotic chiral-symmetry broken phase without quark-bilinear condensate is ruled out from possible QCD vacua. We show that the U(1)B baryon number symmetry is anomalously broken when the {left({mathrm{mathbb{Z}}}_{2{N}_{mathrm{f}}}right)}_{mathrm{A}} discrete axial symmetry and the flavor symmetry are gauged. In the ordinary chiral symmetry breaking, the Skyrmion current turns out to reproduce this ’t Hooft anomaly of massless QCD. In the exotic chiral symmetry breaking, however, the anomalous breaking of U(1)B does not take the correct form, and it is inconsistent with anomaly matching. This no-go theorem is based only on symmetries and anomalies, and thus has a wider range of applicability to the QCD phase diagram than the previous one obtained by QCD inequalities. Lastly, as another application, we check that duality of mathcal{N}=1 supersymmetric QCD with Nf ≥Nc + 1 satisfies the new anomaly matching.

4d mathcal{N} = 1 quiver gauge theories and the An Bailey lemma

We study the integral Bailey lemma associated with the An-root system and identities for elliptic hypergeometric integrals generated thereby. Interpreting integrals as superconformal indices of four-dimensional mathcal{N} = 1 quiver gauge theories with the gauge groups being products of SU(n + 1), we provide evidence for various new dualities. Further confirmation is achieved by explicitly checking that the ‘t Hooft anomaly matching conditions holds. We discuss a flavour symmetry breaking phenomenon for supersymmetric quantum chromodynamics (SQCD), and by making use of the Bailey lemma we indicate its manifestation in a web of linear quivers dual to SQCD that exhibits full s-confinement.

Higher order scheme-independent calculations of physical quantities in the conformal phase of a gauge theory

We consider an asymptotically free vectorial SU($N_c$) gauge theory with $N_f$ massless fermions in a representation $R$, having an infrared fixed point (IRFP) of the renormalization group at $\alpha_{IR}$ in the conformal non-Abelian Coulomb phase. The cases with $R$ equal to the fundamental, adjoint, and symmetric rank-2 tensor representation are considered. We present scheme-independent calculations of the anomalous dimension $\gamma_{\bar\psi\psi,IR}$ to $O(\Delta_f^4)$ and $\beta'_{IR}$ to $O(\Delta_f^5)$ at this IRFP, where $\Delta_f$ is an $N_f$-dependent expansion parameter. Comparisons are made with conventional $n$-loop calculations and lattice measurements. As a test of the accuracy of the $\Delta_f$ expansion, we calculate $\gamma_{\bar\psi\psi,IR}$ to $O(\Delta_f^3)$ in ${\cal N}=1$ SU($N_c$) supersymmetric quantum chromodynamics and find complete agreement, to this order, with the exactly known expression. The $\Delta_f$ expansion also avoids a problem in which an IRFP may not be manifest as an IR zero of a higher $n$-loop beta function.

Applying the Cho–Duam–Ge decomposition to supersymmetric QCD

We study the chromomonopole component of the gluon, as identified by the Cho–Duam–Ge decomposition, in supersymmetric quantum chromodynamics. It is found to be incapable of representing the supersymmetry algebra, leading to supersymmetry breaking. Furthermore, its field strength squared is invariant under the supersymmetry generators. This makes it immune to the positive-definite energy theorem. The energetic favourability of such a condensate is expected in the case of asymptotic freedom. We identify one component of the gluino as the Goldstone fermion.

BPS states in omega background and integrability

We reconsider string and domain wall central charges in N=2 supersymmetric gauge theories in four dimensions in presence of the Omega background in the Nekrasov-Shatashvili (NS) limit. Existence of these charges entails presence of the corresponding topological defects in the theory - vortices and domain walls. In spirit of the 4d/2d duality we discuss the worldsheet low energy effective theory living on the BPS vortex in N=2 Supersymmetric Quantum Chromodynamics (SQCD). We discuss some aspects of the brane realization of the dualities between various quantum integrable models. A chain of such dualities enables us to check the AGT correspondence in the NS limit.

Spontaneous parity breaking and supersymmetry breaking in metastable vacua with consistent

We study the compatibility of spontaneous breaking of parity and successful cosmology in a left-right symmetric model where supersymmetry breaking is achieved in metastable vacua. We show that domain walls formed due to this breaking can be removed due to Planck scale suppressed terms, provided the parity breaking scale $M_R$ is constrained to remain smaller than $10^{10}-10^{11}$ GeV. Ensuring metastability is achieved naturally even if the entire mechanism operates at low scales, within a few orders of magnitude of the TeV scale. Taking $M_R$ as high as permitted, close to the acceptable reheat temperature after inflation, would require the magnetic phase of the Supersymmetric Quantum Chromodynamics (SQCD) to have set in before the end of inflation.

Renormalization effects on the MSSM from a calculable model of a strongly coupled hidden sector

We investigate possible renormalization effects on the low-energy mass spectrum of the minimal supersymmetric standard model (MSSM), using a calculable model of strongly coupled hidden sector. We model the hidden sector by $\mathcal{N}=2$ supersymmetric quantum chromodynamics with gauge group $SU(2)\ifmmode\times\else\texttimes\fi{}U(1)$ and ${N}_{f}=2$ matter hypermultiplets, perturbed by a Fayet-Iliopoulos term which breaks the supersymmetry down to $\mathcal{N}=0$ on a metastable vacuum. In the hidden sector the K\"ahler potential is renormalized. Upon identifying a hidden sector modulus with the renormalization scale, and extrapolating to the strongly coupled regime using the Seiberg-Witten solution, the contribution from the hidden sector to the MSSM renormalization group flows is computed. For concreteness, we consider a model in which the renormalization effects are communicated to the MSSM sector via gauge mediation. In contrast to the perturbative toy examples of hidden sector renormalization studied in the literature, we find that our strongly coupled model exhibits rather intricate effects on the MSSM soft scalar mass spectrum, depending on how the hidden sector fields are coupled to the messenger fields. This model provides a concrete example in which the low-energy spectrum of MSSM particles that are expected to be accessible in collider experiments is obtained using strongly coupled hidden sector dynamics.

On-shell supersymmetry for massive multiplets

The consequences of on-shell supersymmetry are studied for scattering amplitudes with massive particles in four dimensions. Using the massive version of the spinor-helicity formalism, the supersymmetry transformations relating products of on-shell states are derived directly from the on-shell supersymmetry algebra for any massive representation. Solutions to the resulting Ward identities can be constructed as functions on the on-shell superspaces that are obtained from the coherent-state method. In simple cases, it is shown that these superspaces allow one to construct explicitly supersymmetric scattering amplitudes. Supersymmetric on-shell recursion relations for tree-level superamplitudes with massive particles are introduced. As examples, simple supersymmetric amplitudes are constructed in Supersymmetric Quantum Chromodynamics (SQCD), the Abelian Higgs model, the Coulomb branch of $\mathcal{N}=4$, QCD with an effective Higgs-gluon coupling and for massive vector-boson currents.

Non-Abelian monopole-vortex complex

In the context of softly broken N=2 supersymmetric quantum chromodynamics (SQCD), with a hierarchical gauge symmetry breaking SU(N+1) -> U(N) -> 1, at scales v1 and v2, respectively, where v1 >> v2, we construct monopole-vortex complex soliton-like solutions and examine their properties. They represent the minimum of the static energy under the constraint that the monopole and antimonopole positions sitting at the extremes of the vortex are kept fixed. They interpolate the 't Hooft-Polyakov-like regular monopole solution near the monopole centers and a vortex solution far from them and in between. The main result, obtained in the theory with Nf=N equal-mass flavors, is concerned with the existence of exact orientational CP(N-1) zero modes, arising from the exact color-flavor diagonal SU(N)_{C+F} global symmetry. The "unbroken" subgroup SU(N) \subset SU(N+1) with which the na\"ive notion of non-Abelian monopoles and the related difficulties were associated, is explicitly broken at low energies. The monopole transforms nevertheless according to the fundamental representation of a new exact, unbroken SU(N) symmetry group, as does the vortex attached to it. We argue that this explains the origin of the dual non-Abelian gauge symmetry.

OnR-symmetric Fixed Points and Superconformality

An important unanswered question in quantum field theory is to understand precisely under which conditions scale invariance implies invariance under the full conformal group. While the general answer in two dimensions has been known for over twenty years, a precise non-perturbative relation between scale and conformal invariance in higher dimensions has been lacking. In this note, we specialize to four dimensions and give a full quantum mechanical proof that certain unitary R-symmetric fixed points are necessarily superconformal. Among other consequences, this result implies that the infrared fixed points of N=1 supersymmetric quantum chromodynamics are superconformal.

Supersymmetric QCD from noncommutative geometry

We derive supersymmetric quantum chromodynamics from a noncommutative spin manifold. We extend the model of Chamseddine and Connes that leads to the Einstein–Yang–Mills action and apply the spectral action principle to derive the Lagrangian of supersymmetric QCD, including soft supersymmetry breaking (negative sign) mass terms for the squarks. We find that these results are in good agreement with the physics literature.

Supersymmetric QCD and Noncommutative Geometry

We derive supersymmetric quantum chromodynamics from a noncommutative manifold, using the spectral action principle of Chamseddine and Connes. After a review of the Einstein–Yang–Mills system in noncommutative geometry, we establish in full detail that it possesses supersymmetry. This noncommutative model is then extended to give a theory of quarks, squarks, gluons and gluinos by constructing a suitable noncommutative spin manifold (i.e. a spectral triple). The particles are found at their natural place in a spectral triple: the quarks and gluinos as fermions in the Hilbert space, the gluons and squarks as the (bosonic) inner fluctuations of a (generalized) Dirac operator by the algebra of matrix-valued functions on a manifold. The spectral action principle applied to this spectral triple gives the Lagrangian of supersymmetric QCD, including supersymmetry breaking (negative) mass terms for the squarks. We find that these results are in good agreement with the physics literature.

Supersymmetry Breaking in SQCD

It is established that (massive) Supersymmetric Quantum Chromodynamics (SQCD) breaks supersymmetry in a long lived state. We review some of the key properties of this state and motivate the search for alternative models. We outline the dynamics of SQCD with both massive and massless quarks and explain how a drawback of the original models is solved.

N=2cascade revisited and the enhançon bearings

Supergravity backgrounds with varying fluxes generated by fractional branes at nonisolated Calabi-Yau singularities had escaped a precise dual field theory interpretation so far. In the present work, considering the prototypical example of such models, the $\mathbb{C}\ifmmode\times\else\texttimes\fi{}{\mathbb{C}}^{2}/{\mathbb{Z}}_{2}$ orbifold, we propose a solution for this problem, and show that the known cascading solution corresponds to a vacuum on the Coulomb branch of the corresponding quiver gauge theory involving a sequence of strong coupling transitions reminiscent of the baryonic root of $\mathcal{N}=2$ supersymmetric quantum chromodynamics . We also find a slight modification of this cascading vacuum which upon mass deformation is expected to flow to the Klebanov-Strassler cascade. Finally, we discuss an infinite class of vacua on the Coulomb branch whose renormalization group flows include infinitely coupled conformal regimes, and explain their gravitational manifestation in terms of new geometric structures that we dub enhan\ifmmode \mbox{\c{c}}\else \c{c}\fi{}on bearings. Repulson-free backgrounds dual to all the vacua we analyze are explicitly provided.

Matching coefficients for αsandmbto 𝒪(αs2) in the MSSM

We compute the exact two-loop matching coefficients for the strong coupling constant alpha_s and the bottom-quark mass m_b within the Minimal Supersymmetric Standard Model (MSSM), taking into account O(alpha_s^2) contributions from Supersymmetric Quantum Chromodynamics (SQCD). We find that the explicit mass pattern of the supersymmetric particles has a significant impact on the predictions of alpha_s and m_b at high energies. Further on, the three-loop corrections exceed the uncertainty due to the current experimental accuracy. In case of the the running bottom-quark mass, they can reach in the large tan(beta) regime up to 30% of the tree-level value.

Non-Abelian vortices with product moduli

Vortices of a new type, carrying non-Abelian flux moduli $C{P}^{n\ensuremath{-}1}\ifmmode\times\else\texttimes\fi{}C{P}^{r\ensuremath{-}1}$, are found in the context of softly broken $\mathcal{N}=2$ supersymmetric quantum chromodynamics. By tuning the bare quark masses appropriately, we identify the vacuum in which the underlying $SU(N)$ gauge group is partially broken to $SU(n)\ifmmode\times\else\texttimes\fi{}SU(r)\ifmmode\times\else\texttimes\fi{}U(1)/{\mathbb{Z}}_{K}$, where $K$ is the least common multiple of $(n,r)$, and with ${N}_{f}^{su(n)}=n$ and ${N}_{f}^{su(r)}=r$ flavors of light quark multiplets. At much lower energies, the gauge group is broken completely by the squark vacuum expectation values, and vortices develop which carry non-Abelian flux moduli $C{P}^{n\ensuremath{-}1}\ifmmode\times\else\texttimes\fi{}C{P}^{r\ensuremath{-}1}$. For $n>r$, at the length scale at which the $SU(n)$ fluctuations become strongly coupled and Abelianize, the vortex still carries weakly fluctuating $SU(r)$ flux moduli. We discuss the possibility that these vortices are related to the light non-Abelian monopoles found earlier in the fully quantum-mechanical treatment of $4D$ supersymmetric quantum chromodynamics.

High precision calculations within the MSSM

In this talk we report on two recent high precision calculations within the minimal supersymmetric extension of the Standard Model. In the first part of the talk we present the computation of the light CP-even Higgs boson mass with three-loop accuracy, taking into account the next-to-next-to-leading order effects from supersymmetric Quantum Chromodynamics. Furthermore, we discuss a consistent evolution of the strong coupling constant α s from M Z to the GUT scale, involving three-loop running and two-loop decoupling. For both observables the numerical results amount to corrections of the same order as the current experimental accuracy or that expected at the CERN Large Hadron Collider (LHC).