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Kenichi Konishi

Publications and source records attributed to Kenichi Konishi.

At least 55 records · Page 3Linked to original sources
arXiv2012

Singular SQCD Vacua and Confinement

We revisit the study of confining vacua in the softly broken N=2 supersymmetric QCD, in the light of some recent developments in our understanding of the dynamics of N=2 gauge theories. These vacua are characterized by an effective magnetic $SU(r)$ gauge group ($0\leq r\leq N_f/2$) and are referred to sometimes as the $r$ vacua. We further clarify the meaning of $r \leftrightarrow N_{f}-r$ duality arising from the matching of semi-classical and quantum vacua. A particular attention is paid to certain singular SCFT's of N=2 SQCD, driven into confinement phase by the adjoint mass deformation $μ\, Φ^{2}$. In some cases they occur as a result of coalescence of different $r$ vacua as the bare mass is tuned to a critical value.

hep-th↗
arXiv2012

Non-Abelian confinement and the dual gauge symmetry: Many faces of flavor symmetry

We review the physics of confinement based on non-Abelian dual superconductor picture, relying on exact solutions in N=2 supersymmetric QCD and based on the recent developments in our understanding of non-Abelian vortices and monopoles. The non-Abelian monopoles, though they are basically just the 't Hooft-Polyakov SU(2) monopoles embedded in various corners of the larger gauge group, require flavor symmetry in an essential way for their very existence. The phenomenon of flavor-color-flavor separation characterizes the multiple roles flavor symmetry plays in producing quantum-mechanical non-Abelian monopoles.

hep-ph↗
arXiv2012

Supersymmetry Breaking on Gauged Non-Abelian Vortices

There are a large number of systems characterized by a completely broken gauge symmetry, but with an unbroken global color-flavor diagonal symmetry, i.e., systems in the so-called color-flavor locked phase. If the gauge symmetry breaking supports vortices, the latter develop non-Abelian orientational zero-modes and become non-Abelian vortices, a subject of intense study in the last several years. In this paper we consider the effects of weakly gauging the full exact global flavor symmetry in such systems, deriving an effective description of the light excitations in the presence of a vortex. Surprising consequences are shown to follow. The fluctuations of the vortex orientational modes get diffused to bulk modes through tunneling processes. When our model is embedded in a supersymmetric theory, the vortex is still 1/2 BPS saturated, but the vortex effective action breaks supersymmetry spontaneously.

hep-th↗
arXiv2011

Vortices and Monopoles in Mass-deformed SO and USp Gauge Theories

Effects of mass deformations on 1/2 Bogomol'nyi-Prasad-Sommerfield (BPS) non-Abelian vortices are studied in 4d N=2 supersymmetric U(1) \times SO(2n) and U(1) \times USp(2n) gauge theories, with Nf=2n quark multiplets. The 2d N=(2,2) effective worldsheet sigma models on the Hermitian symmetric spaces SO(2n)/U(n) and USp(2n)/U(n) found recently which describe the low-energy excitations of the orientational moduli of the vortices, are generalized to the respective massive sigma models. The continuous vortex moduli spaces are replaced by a finite number (2^{n-1} or 2^{n}) of vortex solutions. The 1/2 BPS kinks connecting different vortex vacua are magnetic monopoles in the 4d theory, trapped inside the vortex core, with total configurations being 1/4 BPS composite states. These configurations are systematically studied within the semi-classical regime.

hep-th↗
arXiv2011

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 naïve 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.

hep-th↗
arXiv2011

Nonabelian Faddeev-Niemi Decomposition of the SU(3) Yang-Mills Theory

Faddeev and Niemi (FN) have introduced an abelian gauge theory which simulates dynamical abelianization in Yang-Mills theory (YM). It contains both YM instantons and Wu-Yang monopoles and appears to be able to describe the confining phase. Motivated by the meson degeneracy problem in dynamical abelianization models, in this note we present a generalization of the FN theory. We first generalize the Cho connection to dynamical symmetry breaking pattern SU(N+1) -> U(N), and subsequently try to complete the Faddeev-Niemi decomposition by keeping the missing degrees of freedom. While it is not possible to write an on-shell complete FN decomposition, in the case of SU(3) theory of physical interest we find an off-shell complete decomposition for SU(3) -> U(2) which amounts to partial gauge fixing, generalizing naturally the result found by Faddeev and Niemi for the abelian scenario SU(N+1) -> U(1)^N. We discuss general topological aspects of these breakings, demonstrating for example that the FN knot solitons never exist when the unbroken gauge symmetry is nonabelian, and recovering the usual no-go theorems for colored dyons.

hep-th↗
arXiv2010

Monopole-vortex complex in a theta vacuum

We discuss aspects of the monopole-vortex complex soliton arising in a hierarchically broken gauge system, G to H to 1, in a theta vacuum of the underlying G theory. Here we focus our attention mainly on the simplest such system with G=SU(2) and H=U(1). A consistent picture of the effect of the theta parameter is found both in a macroscopic, dual picture and in a microscopic description of the monopole-vortex complex soliton.

hep-th↗
arXiv2010

Group Theory of Non-Abelian Vortices

We investigate the structure of the moduli space of multiple BPS non-Abelian vortices in U(N) gauge theory with N fundamental Higgs fields, focusing our attention on the action of the exact global (color-flavor diagonal) SU(N) symmetry on it. The moduli space of a single non-Abelian vortex, CP(N-1), is spanned by a vector in the fundamental representation of the global SU(N) symmetry. The moduli space of winding-number k vortices is instead spanned by vectors in the direct-product representation: they decompose into the sum of irreducible representations each of which is associated with a Young tableau made of k boxes, in a way somewhat similar to the standard group composition rule of SU(N) multiplets. The Kähler potential is exactly determined in each moduli subspace, corresponding to an irreducible SU(N) orbit of the highest-weight configuration.

hep-th↗
arXiv2010

Non-Abelian vortex dynamics: Effective world-sheet action

The low-energy vortex effective action is constructed in a wide class of systems in a color-flavor locked vacuum, which generalizes the results found earlier in the context of U(N) models. It describes the weak fluctuations of the non-Abelian orientational moduli on the vortex worldsheet. For instance, for the minimum vortex in SO(2N) x U(1) or USp(2N) x U(1) gauge theories, the effective action found is a two-dimensional sigma model living on the Hermitian symmetric spaces SO(2N)/U(N) or USp(2N)/U(N), respectively. The fluctuating moduli have the structure of that of a quantum particle state in spinor representations of the GNO dual of the color-flavor SO(2N) or USp(2N) symmetry, i.e. of SO(2N) or of SO(2N+1). Applied to the benchmark U(N) model our procedure reproduces the known CP(N-1) worldsheet action; our recipe allows us to obtain also the effective vortex action for some higher-winding vortices in U(N) and SO(2N) theories.

hep-th↗
arXiv2010

Low-energy U(1) x USp(2M) gauge theory from simple high-energy gauge group

We give an explicit example of the embedding of a near BPS low-energy (U(1) x USp(2M))/Z_2 gauge theory into a high-energy theory with a simple gauge group and adjoint matter content. This system possesses degenerate monopoles arising from the high-energy symmetry breaking as well as non-Abelian vortices due to the symmetry breaking at low energies. These solitons of different codimensions are related by the exact homotopy sequences.

hep-th↗
arXiv2010

New Results on Non-Abelian Vortices - further insights into monopole, vortex and confinement

We discuss some of the latest results concerning the non-Abelian vortices. The first concerns the construction of non-Abelian BPS vortices based on general gauge groups of the form G= G' x U(1). In particular detailed results about the vortex moduli space have been obtained for G'=SO(N) or USp(2N). The second result is about the "fractional vortices", i.e., vortices of the minimum winding but having substructures in the tension (or flux) density in the transverse plane. Thirdly, we discuss briefly the monopole-vortex complex.

hep-th↗
arXiv2009

On Confinement Index

The smallest integer t for which the Wilson loop W^{t} fails to exhibit area law is known as the confinement index of a given field theory. The confinement index provides us with subtle information on the vacuum properties of the system. We study the behavior of the Wilson and 't Hooft loops and compute the confinement index in a wide class of N=1 supersymmetric gauge theories. All possible electric and magnetic screenings are taken into account. The results found are consistent with the theta periodicity, and whenever such a check is available, with the factorization property of Seiberg-Witten curves.

hep-th↗
arXiv2009

Fractional Vortices and Lumps

We study what might be called fractional vortices, vortex configurations with the minimum winding from the viewpoint of their topological stability, but which are characterized by various notable substructures in the transverse energy distribution. The fractional vortices occur in diverse Abelian or non-Abelian generalizations of the Higgs model. The global and local features characterizing these are studied, and we identify the two crucial ingredients for their occurrence - the vacuum degeneracy leading to non-trivial vacuum moduli M, and the BPS nature of the vortices. Fractional vortices are further classified into two kinds. The first type of such vortices appear when M has orbifold Z_n singularities; the second type occurs in systems in which the vacuum moduli space M possesses either a deformed geometry or some singularity. These general features are illustrated with several concrete models.

hep-th↗
arXiv2009

Non-Abelian Vortices in SO(N) and USp(N) Gauge Theories

Non-Abelian BPS vortices in SO(N) x U(1) and USp(2N) x U(1) gauge theories are constructed in maximally color-flavor locked vacua. We study in detail their moduli and transformation properties under the exact symmetry of the system. Our results generalize non-trivially those found earlier in supersymmetric U(N) gauge theories. The structure of the moduli spaces turns out in fact to be considerably richer here than what was found in the U(N) theories. We find that vortices are generally of the semi-local type, with power-like tails of profile functions.

hep-th↗
arXiv2009

On the Stability of Non-Abelian Semi-local Vortices

We study the stability of non-Abelian semi-local vortices based on an N=2 supersymmetric H = [SU(Nc) x U(1)]/Z_Nc = U(Nc) gauge theory with an arbitrary number of flavors (Nf > Nc) in the fundamental representation, when certain N=1 mass terms are present, making the vortex solutions no longer BPS-saturated. Local (ANO-like) vortices are found to be stable against fluctuations in the transverse directions. Strong evidence is found that the ANO-like vortices are actually the true minima. In other words, the semi-local moduli, which are present in the BPS limit, disappear in our non-BPS system, leaving the vortex with the orientational moduli CP(Nc-1) only. We discuss the implications of this fact on the system in which the U(Nc) model arises as the low-energy approximation of an underlying e.g. G = SU(Nc+1) gauge theory.

hep-th↗
arXiv2008

The Magnetic Monopole Seventy-Five Years Later

Non-Abelian monopoles are present in the fully quantum mechanical low-energy effective action of many solvable supersymmetric theories. They behave perfectly as pointlike particles carrying non-Abelian dual magnetic charges. They play a crucial role in confinement and in dynamical symmetry breaking in these theories. There is a natural identification of these excitations within the semiclassical approach, which involves the flavor symmetry in an essential manner. We review, in an introductory fashion, the recent development which has led to a better understanding of the nature of non-Abelian monopoles and of their role in confinement and dynamical symmetry breaking in strongly interacting theories.

hep-th↗
arXiv2008

Vortices which do not Abelianize dynamically: Semi-classical origin of non-Abelian monopoles

After briefly reviewing the problems associated with non-Abelian monopoles, we turn our attention to the development in our understanding of non-Abelian {\it vortices} in the last several years. In the U(N) model with $N_{f}=N$ flavors in which they were first found, the fluctuations of the orientational modes along the vortex length and in time become strongly coupled at long distances. They effectively reduce to Abelian ANO vortices. We discuss then a very recent work on non-Abelian vortices with $CP^{n-1}\times CP^{r-1}$ orientational moduli, which, unlike the ones so far extensively studied, do not dynamically Abelianize completely. The surviving vortex orientational moduli, fluctuating along the vortex length and in time, gets absorbed by the monopoles at the ends, turning into the dual gauge degrees of freedom for the latter.

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