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H. Itoyama

Publications and source records attributed to H. Itoyama.

At least 37 records · Page 2Linked to original sources
arXiv2014

126 GeV Higgs Boson Associated with D-term Triggered Dynamical Supersymmetry Breaking

Continuing with our previous work on D-term triggered dynamical supersymmetry breaking, we consider a system in which our generic N=1 action is minimally extended to include the pair of Higgs doublet superfields charged under the overall U(1) as well as mu and B mu terms. The gauge group is taken to be SU(3)_C times SU(2)_L times U(1)_Y times U(1). We point out, among other things, that the Higgs mass less than the Z-boson mass at tree level can be pushed up to be around 126 GeV by D-term contributions of the overall U(1). This is readily realized by taking a U(1) gauge coupling of O(1).

hep-ph↗
arXiv2014

Mass Sum Rule of the Effective Action on Vacua with Broken Rigid N=1 Supersymmetry

We present an extension of the mass sum rule that applies to renormalizable rigid supersymmetric field theories to the case of the N=1 supersymmetric effective action (the gauged non-linear sigma model) consisting of adjoint scalar superfields and vector superfields possessing a K"ahler potential, a set of gauge coupling functions (second prepotential derivatives) and a superpotential, which respectively set their energy scales. The mass sum rule derived is valid for any vacua, including the (metastable) one of broken supersymmetry with the condensates of D-term and/or F-term. We manage to extend these analyses to the cases where superfields in (anti-)fundamental representation are present. The supertrace is shown to vanish in those cases where underlying geometry is special K"ahler and theory under concern is anomaly free. Simple phenomenological application is given, providing an upper bound for gaugino masses. We discuss that the effects of the D and/or F condensates can be represented as a set of soft breaking terms with their strengths predicted by the scales.

hep-th↗
arXiv2014

Matching branches of non-perturbative conformal block at its singularity divisor

Conformal block is a function of many variables, usually represented as a formal series, with coefficients which are certain matrix elements in the chiral (e.g. Virasoro) algebra. Non-perturbative conformal block is a multi-valued function, defined globally over the space of dimensions, with many branches and, perhaps, additional free parameters, not seen at the perturbative level. We discuss additional complications of non-perturbative description, caused by the fact that all the best studied examples of conformal blocks lie at the singularity locus in the moduli space (at divisors of the coefficients or, simply, at zeroes of the Kac determinant). A typical example is the Ashkin-Teller point, where at least two naive non-perturbative expressions are provided by elliptic Dotsenko-Fateev integral and by the celebrated Zamolodchikov formula in terms of theta-constants, and they are different. The situation is somewhat similar at the Ising and other minimal model points.

hep-th↗
arXiv2013

D-term Triggered Dynamical Supersymmetry Breaking

We present the mechanism of the dynamical supersymmetry breaking at the metastable vacuum recently uncovered in the N=1 U(N) supersymmetric gauge theory that contains adjoint superfields and that is specified by Kahler and non-canonical gauge kinetic functions and a superpotential whose tree vacua preserve N=1 supersymmetry. The overall U(1) serves as the hidden sector and no messenger superfield is required. The dynamical supersymmetry breaking is triggered by the non-vanishing D term coupled to the observable sector, and is realized by the self-consistent Hartree-Fock approximation of the NJL type while it eventually brings us the non-vanishing F term as well. It is shown that theoretical analysis is resolved as a variational problem of the effective potential for three kinds of background fields, namely, the complex scalar, and the two order parameters D and F of supersymmetry, the last one being treated perturbatively. We determine the stationary point and numerically check the consistency of such treatment as well as the local stability of the scalar potential. The coupling to the N = 1 supergravity is given and the gravitino mass formula is derived.

hep-ph↗
arXiv2012

Eigenvalue hypothesis for Racah matrices and HOMFLY polynomials for 3-strand knots in any symmetric and antisymmetric representations

Character expansion expresses extended HOMFLY polynomials through traces of products of finite dimensional R- and Racah mixing matrices. We conjecture that the mixing matrices are expressed entirely in terms of the eigenvalues of the corresponding R-matrices. Even a weaker (and, perhaps, more reliable) version of this conjecture is sufficient to explicitly calculate HOMFLY polynomials for all the 3-strand braids in arbitrary (anti)symmetric representations. We list the examples of so obtained polynomials for V=[3] and V=[4], and they are in accordance with the known answers for torus and figure-eight knots, as well as for the colored special and Jones polynomials. This provides an indirect evidence in support of our conjecture.

math-ph↗
arXiv2012

Character expansion for HOMFLY polynomials. III. All 3-Strand braids in the first symmetric representation

We continue the program of systematic study of extended HOMFLY polynomials. Extended polynomials depend on infinitely many time variables, are close relatives of integrable tau-functions, and depend on the choice of the braid representation of the knot. They possess natural character decompositions, with coefficients which can be defined by exhaustively general formula for any particular number m of strands in the braid and any particular representation R of the Lie algebra GL(\infty). Being restricted to "the topological locus" in the space of time variables, the extended HOMFLY polynomials reproduce the ordinary knot invariants. We derive such a general formula, for m=3, when the braid is parameterized by a sequence of integers (a_1,b_1,a_2,b_2,...), and for the first non-fundamental representation R=[2]. Instead of calculating the mixing matrices directly, we deduce them from comparison with the known answers for torus and composite knots. A simple reflection symmetry converts the answer for the symmetric representation [2] into that for the antisymmetric one [1,1]. The result applies, in particular, to the figure eight knot 4_1, and was further extended to superpolynomials in arbitrary symmetric and antisymmetric representations in arXiv:1203.5978.

hep-th↗
arXiv2012

D-term Dynamical Supersymmetry Breaking Generating Split N=2 Gaugino Masses of Mixed Majorana-Dirac Type

Under a few mild assumptions, N=1 supersymmetry in four dimensions is shown to be spontaneously broken in a self-consistent Hartree-Fock approximation of BCS/NJL type to one-loop off-shell, in the gauge theory specified by the gauge kinetic function and the superpotential of adjoint chiral superfields, in particular, that possesses N=2 extended supersymmetry spontaneously broken to N=1 at tree level. The N=2 gauginos receive mixed Majorana-Dirac masses and are split. We derive an explicit form of the gap equation, showing the existence of a nontrivial solution.

hep-ph↗
arXiv2012

HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations

Explicit answer is given for the HOMFLY polynomial of the figure eight knot $4_1$ in arbitrary symmetric representation R=[p]. It generalizes the old answers for p=1 and 2 and the recently derived results for p=3,4, which are fully consistent with the Ooguri-Vafa conjecture. The answer can be considered as a quantization of the σ_R = σ_{[1]}^{|R|} identity for the "special" polynomials (they define the leading asymptotics of HOMFLY at q=1), and arises in a form, convenient for comparison with the representation of the Jones polynomials as sums of dilogarithm ratios. In particular, we construct a difference equation ("non-commutative A-polynomial") in the representation variable p. Simple symmetry transformation provides also a formula for arbitrary antisymmetric (fundamental) representation R=[1^p], which also passes some obvious checks. Also straightforward is a deformation from HOMFLY to superpolynomials. Further generalizations seem possible to arbitrary Young diagrams R, but these expressions are harder to test because of the lack of alternative results, even partial.

hep-th↗
arXiv2010

Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type

We consider a series of massive scaling limits m_1 -> infty, q -> 0, lim m_1 q = Lambda_{3} followed by m_4 -> infty, Lambda_{3} -> 0, lim m_4 Lambda_{3} = (Lambda_2)^2 of the beta-deformed matrix model of Selberg type (N_c=2, N_f=4) which reduce the number of flavours to N_f=3 and subsequently to N_f=2. This keeps the other parameters of the model finite, which include n=N_L and N=n+N_R, namely, the size of the matrix and the "filling fraction". Exploiting the method developed before, we generate instanton expansion with finite g_s, epsilon_{1,2} to check the Nekrasov coefficients (N_f =3,2 cases) to the lowest order. The limiting expressions provide integral representation of irregular conformal blocks which contains a 2d operator lim frac{1}{C(q)} : e^{(1/2) α_1 ϕ(0)}: (int_0^q dz : e^{b_E phi(z)}:)^n : e^{(1/2) alpha_2 phi(q)}: and is subsequently analytically continued.

hep-th↗
arXiv2008

Deviation from Alday-Maldacena Duality For Wavy Circle

Alday-Maldacena conjecture is that the area A_P of the minimal surface in AdS_5 space with a boundary P, located in Euclidean space at infinity of AdS_5, coincides with a double integral D_P along P, the Abelian Wilson average in an auxiliary dual model. The boundary P is a polygon formed by momenta of n external light-like particles in N=4 SYM theory, and in a certain n=infty limit it can be substituted by an arbitrary smooth curve (wavy circle). The Alday-Maldacena conjecture is known to be violated for n>5, when it fails to be supported by the peculiar global conformal invariance, however, the structure of deviations remains obscure. The case of wavy lines can appear more convenient for analysis of these deviations due to the systematic method developed in arXiv:0803.1547 for (perturbative) evaluation of minimal areas, which is not yet available in the presence of angles at finite n. We correct a mistake in that paper and explicitly evaluate the h^2\bar h^2 terms, where the first deviation from the Alday-Maldacena duality arises for the wavy circle.

hep-th↗
arXiv2008

"Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle

If the Alday-Maldacena version of string/gauge duality is formulated as an equivalence between double loop and area integrals a la arXiv: 0708.1625, then this pure geometric relation can be tested for various choices of n-side polygons. The simplest possibility arises at n=infinity, with polygon substituted by an arbitrary continuous curve. If the curve is a circle, the minimal surface problem is exactly solvable. If it infinitesimally deviates from a circle, then the duality relation can be studied by expanding in powers of a small parameter. In the first approximation the Nambu-Goto (NG) equations can be linearized, and the peculiar NG Laplacian plays the central role. Making use of explicit zero-modes of this operator (NG-harmonic functions), we investigate the geometric duality in the lowest orders for small deformations of arbitrary shape lying in the plane of the original circle. We find a surprisingly strong dependence of the minimal area on regularization procedure affecting "the boundary terms" in minimal area. If these terms are totally omitted, the remaining piece is regularization independent, but still differs by simple numerical factors like 4 from the double-loop integral which represents the BDS formula so that we stop short from the first non-trivial confirmation of the Alday-Maldacena duality. This confirms the earlier-found discrepancy for two parallel lines at n=infinity, but demonstrates that it actually affects only a finite number (out of infinitely many) of parameters in the functional dependence on the shape of the boundary, and the duality is only slightly violated, which allows one to call this violation an anomaly.

hep-th↗
arXiv2007

Boundary Ring or a Way to Construct Approximate NG Solutions with Polygon Boundary Conditions. II. Polygons which admit an inscribed circle

We further develop the formalism of arXiv:0712.0159 for approximate solution of Nambu-Goto (NG) equations with polygon conditions in AdS backgrounds, needed in modern studies of the string/gauge duality. Inscribed circle condition is preserved, which leaves only one unknown function y_0(y_1,y_2) to solve for, what considerably simplifies our presentation. The problem is to find a delicate balance -- if not exact match -- between two different structures: NG equation -- a non-linear deformation of Laplace equation with solutions non-linearly deviating from holomorphic functions, -- and the boundary ring, associated with polygons made from null segments in Minkovski space. We provide more details about the theory of these structures and suggest an extended class of functions to be used at the next stage of Alday-Maldacena program: evaluation of regularized NG actions.

hep-th↗
arXiv2007

Boundary Ring: a way to construct approximate NG solutions with polygon boundary conditions: I. Z_n-symmetric configurations

We describe an algebro-geometric construction of polygon-bounded minimal surfaces in ADS_5, based on consideration of what we call the "boundary ring" of polynomials. The first non-trivial example of the Nambu-Goto (NG) solutions for Z_6-symmetric hexagon is considered in some detail. Solutions are represented as power series, of which only the first terms are evaluated. The NG equations leave a number of free parameters (a free function). Boundary conditions, which fix the free parameters, are imposed on truncated series. It is still unclear if explicit analytic formulas can be found in this way, but even approximate solutions, obtained by truncation of power series, can be sufficient to investigate the Alday-Maldacena -- BDS/BHT version of the string/gauge duality.

hep-th↗
arXiv2006

The AdS_5 x S^5 superstrings in the generalized light-cone gauge

The kappa-symmetry-fixed Green-Schwarz action in the AdS_5 x S^5 background is treated canonically in a version of the light-cone gauge. After reviewing the generalized light-cone gauge for a bosonic sigma model, we present the Hamiltonian dynamics of the Green-Schwarz action by using the transverse degrees of freedom. The remaining fermionic constraints are all second class, which we treat by the Dirac bracket. Upon quantization, all of the transverse coordinates are inevitably non-commutative.

hep-th↗
arXiv2006

Partition Functions of Reduced Matrix Models with Classical Gauge Groups

We evaluate partition functions of matrix models which are given by topologically twisted and dimensionally reduced actions of d=4 N=1 super Yang-Mills theories with classical (semi-)simple gauge groups, SO(2N), SO(2N+1) and USp(2N). The integrals reduce to those over the maximal tori by semi-classical approximation which is exact in reduced models. We carry out residue calculus by developing a diagrammatic method, in which the action of the Weyl groups and therefore counting of multiplicities are explained obviously.

hep-th↗
arXiv2004

Whitham Prepotential and Superpotential

N=2 supersymmetric U(N) Yang-Mills theory softly broken to N=1 by the superpotential of the adjoint scalar fields is discussed from the viewpoint of the Whitham deformation theory for prepotential. With proper identification of the superpotential we derive the matrix model curve from the condition that the mixed second derivatives of the Whitham prepotential have a nontrivial kernel.

hep-th↗
arXiv2003

Supereigenvalue Model and Dijkgraaf-Vafa Proposal

We present a variant of the supereigenvalue model proposed before by Alvarez-Gaume, Itoyama, Manes, and Zadra. This model derives a set of three planar loop equations which takes the same form as the set of three anomalous Ward-Takahashi identities on the gaugino condensates recently derived by Cachazo, Douglas, Seiberg and Witten. Another model which implements N=2 superVirasoro constraints is constructed for comparison.

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