arXiv subjects

Keisuke Ohashi

Publications and source records attributed to Keisuke Ohashi.

At least 55 records · Page 3Linked to original sources

arXiv2009

SO and USp Kahler and Hyper-Kahler Quotients and Lumps

We study non-linear sigma models whose target spaces are the Higgs phases of supersymmetric SO and USp gauge theories by using the Kahler and hyper-Kahler quotient constructions. We obtain the explicit Kahler potentials and develop an expansion formula to make use of the obtained potentials from which we also calculate the curvatures of the manifolds. The 1/2 BPS lumps in the U(1) x SO and U(1) x USp Kahler quotients and their effective descriptions are also studied. In this connection, a general relation between moduli spaces of vortices and lumps is discussed. We find a new singular limit of the lumps with non-vanishing sizes in addition to the ordinary small lump singularity. The former is due to the existence of singular submanifolds in the target spaces.

hep-th↗

arXiv2009

Multiple Layer Structure of Non-Abelian Vortex

Bogomol'nyi-Prasad-Sommerfield (BPS) vortices in U(N) gauge theories have two layers corresponding to non-Abelian and Abelian fluxes, whose widths depend nontrivially on the ratio of U(1) and SU(N) gauge couplings. We find numerically and analytically that the widths differ significantly from the Compton lengths of lightest massive particles with the appropriate quantum number.

hep-th↗

arXiv2008

Dynamics of Strings between Walls

Configurations of vortex-strings stretched between or ending on domain walls were previously found to be 1/4 Bogomol'nyi-Prasad-Sommerfield(BPS) states in N=2 supersymmetric gauge theories in 3+1 dimensions. Among zero modes of string positions, the center of mass of strings in each region between two adjacent domain walls is shown to be non-normalizable whereas the rests are normalizable. We study dynamics of vortex-strings stretched between separated domain walls by using two methods, the moduli space (geodesic) approximation of full 1/4 BPS states and the charged particle approximation for string endpoints in the wall effective action. In the first method we explicitly obtain the effective Lagrangian, in terms of hypergeometric functions, and find the 90 degree scattering for head-on collision. In the second method the domain wall effective action is assumed to be U(1)^N gauge theory, and we find a good agreement between two methods for well separated strings.

hep-th↗

arXiv2008

Non-Abelian Vortices without Dynamical Abelianization

Vortices carrying truly non-Abelian flux moduli, which do not dynamically reduce to Abelian vortices, are found in the context of softly-broken ${\cal N}=2$ supersymmetric chromodynamics (SQCD). By tuning the bare quark masses appropriately we identify the vacuum in which the underlying SU(N) gauge group is partially broken to $SU(n) \times SU(r) \times U(1)/{\mathbbm Z}_{K}$, 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 VEVs, and vortices develop which carry non-Abelian flux moduli $CP^{n-1}\times CP^{r-1}$. For $n>r$ we argue that the SU(n) fluctuations become strongly coupled and Abelianize, while leaving weakly fluctuating $SU(r)$ flux moduli. This allows us to recognize the semi-classical origin of the light non-Abelian monopoles found earlier in the fully quantum-mechanical treatment of 4D SQCD.

hep-th↗

arXiv2008

Domain Walls with Non-Abelian Clouds

Domain walls in U(N) gauge theories, coupled to Higgs scalar fields with degenerate masses, are shown to possess normalizable non-Abelian Nambu-Goldstone(NG) modes, which we call non-Abelian clouds. We construct the moduli space metric and its Kahler potential of the effective field theory on the domain walls, by focusing on two models: a U(1) gauge theory with several charged Higgs fields, and a U(N) gauge theory with 2N Higgs fields in the fundamental representation. We find that non-Abelian clouds spread between two domain walls and that their rotation induces long-range repulsive force, in contrast to a U(1) mode in models with fully non-degenerate masses which gives short-range force. We also construct a bound state of dyonic domain walls by introducing the imaginary part of the Higgs masses. In the latter model we find that when all walls coincide SU(N)_L x SU(N)_R x U(1) symmetry is broken down to SU(N)_V, and U(N)_A NG modes and the same number of quasi-NG modes are localized on the wall. When n walls separate, off diagonal elements of U(n) NG modes have wave functions spreading between two separated walls (non-Abelian clouds), whereas some quasi-NG modes turn to NG bosons as a result of further symmetry breaking U(n)_V --> U(1)_V^n. In the case of 4+1 dimensional bulk, we can dualize the effective theory to the supersymmetric Freedman-Townsend model of non-Abelian 2-form fields.

hep-th↗

arXiv2008

Constructing Non-Abelian Vortices with Arbitrary Gauge Groups

We construct the general vortex solution in the fully-Higgsed, color-flavor locked vacuum of a non-Abelian gauge theory, where the gauge group is taken to be the product of an arbitrary simple group and U(1), with a Fayet-Iliopoulos term. The vortex moduli space is determined.

hep-th↗

arXiv2007

Comments on Charges and Near-Horizon Data of Black Rings

We study how the charges of the black rings measured at the asymptotic infinity are encoded in the near-horizon metric and gauge potentials, independent of the detailed structure of the connecting region. Our analysis clarifies how different sets of four-dimensional charges can be assigned to a single five-dimensional object under the Kaluza-Klein reduction. Possible choices are related by the Witten effect on dyons and by the large gauge transformation in four and five dimensions, respectively.

hep-th↗

arXiv2007

Effective Lagrangian of Domain Wall Networks

Domain wall networks are studied in N=2 supersymmetric U(N_C) gauge theory with N_F (>N_C) flavors. We find a systematic method to construct domain wall networks in terms of moduli matrices. Normalizable moduli parameters of the network are found to be sizes and phases of the loop. We obtain moduli space metric which specifies the effective Lagrangian on the domain wall networks. It is used to study dynamics of domain wall networks with the moduli approximation.

hep-th↗

arXiv2007

Dynamics of Domain Wall Networks

Networks or webs of domain walls are admitted in Abelian or non-Abelian gauge theory coupled to fundamental Higgs fields with complex masses. We examine the dynamics of the domain wall loops by using the moduli approximation and find a phase rotation induces a repulsive force which can be understood as a Noether charge of Q-solitons. Non-Abelian gauge theory allows different types of loops which can be deformed to each other by changing a modulus. This admits the moduli geometry like a sandglass made by gluing the tips of the two cigar-(cone-)like metrics of a single triangle loop. We conclude that the sizes of all loops tend to grow for a late time in general models with complex Higgs masses, while the sizes are stabilized at some values once triplet masses are introduced for the Higgs fields. We also show that the stationary motion on the moduli space of the domain wall webs represents 1/4 BPS Q-webs of walls.

hep-th↗

arXiv2007

On the moduli space of semilocal strings and lumps

We study BPS non-abelian semilocal vortices in U(Nc) gauge theory with Nf flavors, Nf > Nc, in the Higgs phase. The moduli space for arbitrary winding number is described using the moduli matrix formalism. We find a relation between the moduli spaces of the semilocal vortices in a Seiberg-like dual pairs of theories, U(Nc) and U(Nf-Nc). They are two alternative regularizations of a "parent" non-Hausdorff space, which tend to the same moduli space of sigma-model lumps in the infinite gauge coupling limits. We examine the normalizability of the zero-modes and find the somewhat surprising phenomenon that the number of normalizable zero-modes, dynamical fields in the effective action, depends on the point of the moduli space we are considering. We find, in the lump limit, an effective action on the vortex worldsheet, which we compare to that found by Shifman and Yung.

hep-th↗

arXiv2007

Non-Abelian duality from vortex moduli: a dual model of color-confinement

It is argued that the dual transformation of non-Abelian monopoles occurring in a system with gauge symmetry breaking G -> H is to be defined by setting the low-energy H system in Higgs phase, so that the dual system is in confinement phase. The transformation law of the monopoles follows from that of monopole-vortex mixed configurations in the system (with a large hierarchy of energy scales, v_1 >> v_2) G -> H -> 0, under an unbroken, exact color-flavor diagonal symmetry H_{C+F} \sim {\tilde H}. The transformation property among the regular monopoles characterized by π_2(G/H), follows from that among the non-Abelian vortices with flux quantized according to π_1(H), via the isomorphism π_1(G) \sim π_1(H) / π_2(G/H). Our idea is tested against the concrete models -- softly-broken {\cal N}=2 supersymmetric SU(N), SO(N) and USp(2N) theories, with appropriate number of flavors. The results obtained in the semiclassical regime (at v_1 >> v_2 >> Λ) of these models are consistent with those inferred from the fully quantum-mechanical low-energy effective action of the systems (at v_1, v_2 \sim Λ).

hep-th↗

arXiv2007

Supersymmetric Completion of an R^2 Term in Five-Dimensional Supergravity

We analyze the structure of a particular higher derivative correction of five-dimensional ungauged and gauged supergravity with eight supercharges. Specifically, we determine all the purely bosonic terms which are connected by the supersymmetry transformation to the mixed gauge-gravitational Chern-Simons term, W wedge tr R wedge R. Our construction utilizes the superconformal formulation of supergravity. As an application, we determine the condition for the supersymmetric anti-de Sitter vacuum with this term. We check that it gives precisely the same condition as the a-maximization in four-dimensional superconformal field theory on the boundary, as predicted by the AdS/CFT correspondence.

hep-th↗

arXiv2007

Universal Reconnection of Non-Abelian Cosmic Strings

We show that local/semilocal strings in Abelian/non-Abelian gauge theories with critical couplings always reconnect classically in collision, by using moduli space approximation. The moduli matrix formalism explicitly identifies a well-defined set of the vortex moduli parameters. Our analysis of generic geodesic motion in terms of those shows right-angle scattering in head-on collision of two vortices, which is known to give the reconnection of the strings.

hep-th↗

arXiv2007

Statistical Mechanics of Vortices from D-branes and T-duality

We propose a novel and simple method to compute the partition function of statistical mechanics of local and semi-local BPS vortices in the Abelian-Higgs model and its non-Abelian extension on a torus. We use a D-brane realization of the vortices and T-duality relation to domain walls. We there use a special limit where domain walls reduce to gas of hard (soft) one-dimensional rods for Abelian (non-Abelian) cases. In the simpler cases of the Abelian-Higgs model on a torus, our results agree with exact results which are geometrically derived by an explicit integration over the moduli space of vortices. The equation of state for U(N) gauge theory deviates from van der Waals one, and the second virial coefficient is proportional to 1/sqrt{N}, implying that non-Abelian vortices are "softer" than Abelian vortices. Vortices on a sphere are also briefly discussed.

hep-th↗

arXiv2007

Effective Lagrangians on Domain Walls and Other Solitons

Maintaining the preserved supersymmetry helps to find the effective Lagrangian on the BPS background in gauge theories with eight supercharges. As concrete examples, we take 1/2 BPS domain walls. The Lagrangian is given in terms of the superfields with manifest four preserved supercharges and is expanded in powers of the slow-movement parameter lambda. The O(lambda^0) gives the superfield form of the BPS equations, whereas all the fluctuation fields follow at O(lambda^1). The effective Lagrangian is given by the density of the K"ahler potential which emerges automatically from the lambda expansion making four preserved supercharges manifest. More complete account of our method and applications is given in hep-th/0602289 in which the case of non-Abelian vortices is also worked out.

hep-th↗

arXiv2007

Effective Action of Domain Wall Networks

U(Nc) gauge theory with Nf fundamental scalars admits BPS junctions of domain walls. When the networks/webs of these walls contain loops, their size moduli give localized massless modes. We construct Kahler potential of their effective action. In the large size limit Kahler metric is well approximated by kinetic energy of walls and junctions, which is understood in terms of tropical geometry. Kahler potential can be expressed in terms of hypergeometric functions which are useful to understand small size behavior. Even when the loop shrinks, the metric is regular with positive curvature. Moduli space of a single triangle loop has a geometry between a cone and a cigar.

hep-th↗

arXiv2006

Non-Abelian Vortices of Higher Winding Numbers

We make a detailed study of the moduli space of winding number two (k=2) axially symmetric vortices (or equivalently, of co-axial composite of two fundamental vortices), occurring in U(2) gauge theory with two flavors in the Higgs phase, recently discussed by Hashimoto-Tong (hep-th/0506022) and Auzzi-Shifman-Yung (hep-th/0511150). We find that it is a weighted projective space WCP^2_(2,1,1)=CP^2/Z_2. This manifold contains an A_1-type (Z_2) orbifold singularity even though the full moduli space including the relative position moduli is smooth. The SU(2) transformation properties of such vortices are studied. Our results are then generalized to U(N) gauge theory with N flavors, where the internal moduli space of k=2 axially symmetric vortices is found to be a weighted Grassmannian manifold. It contains singularities along a submanifold.

hep-th↗

arXiv2006

1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --

We systematically classify 1/2, 1/4 and 1/8 BPS equations in SUSY gauge theories in d=6, 5, 4, 3 and 2 with eight supercharges, with gauge groups and matter contents being arbitrary. Instantons (strings) and vortices (3-branes) are only allowed 1/2 BPS solitons in d=6 with N=1 SUSY. We find two 1/4 BPS equations and the unique 1/8 BPS equation in d=6 by considering configurations made of these field theory branes. All known BPS equations are rederived while several new 1/4 and 1/8 BPS equations are found in dimension less than six by dimensional reductions.

hep-th↗