Instantons and Yang-Mills Flows on Coset Spaces

We consider the Yang-Mills flow equations on a reductive coset space G/H and the Yang-Mills equations on the manifold R x G/H. On nonsymmetric coset spaces G/H one can introduce geometric fluxes identified with the torsion of the spin connection. The condition of G-equivariance imposed on the gauge fields reduces the Yang-Mills equations to phi^4-kink equations on R. Depending on the boundary conditions and torsion, we obtain solutions to the Yang-Mills equations describing instantons, chains of instanton-anti-instanton pairs or modifications of gauge bundles. For Lorentzian signature on R x G/H, dyon-type configurations are constructed as well. We also present explicit solutions to the Yang-Mills flow equations and compare them with the Yang-Mills solutions on R x G/H.Comment: 1+12 page

Some Applications of the Lee-Yang Theorem

For lattice systems of statistical mechanics satisfying a Lee-Yang property (i.e., for which the Lee-Yang circle theorem holds), we present a simple proof of analyticity of (connected) correlations as functions of an external magnetic field h, for Re h > 0 or Re h < 0. A survey of models known to have the Lee-Yang property is given. We conclude by describing various applications of the aforementioned analyticity in h.Comment: 16 page

String theories as the adiabatic limit of Yang-Mills theory

We consider Yang-Mills theory with a matrix gauge group $G$ on a direct product manifold $M=\Sigma_2\times H^2$, where $\Sigma_2$ is a two-dimensional Lorentzian manifold and $H^2$ is a two-dimensional open disc with the boundary $S^1=\partial H^2$. The Euler-Lagrange equations for the metric on $\Sigma_2$ yield constraint equations for the Yang-Mills energy-momentum tensor. We show that in the adiabatic limit, when the metric on $H^2$ is scaled down, the Yang-Mills equations plus constraints on the energy-momentum tensor become the equations describing strings with a worldsheet $\Sigma_2$ moving in the based loop group $\Omega G=C^\infty (S^1, G)/G$, where $S^1$ is the boundary of $H^2$. By choosing $G=R^{d-1, 1}$ and putting to zero all parameters in $\Omega R^{d-1, 1}$ besides $R^{d-1, 1}$, we get a string moving in $R^{d-1, 1}$. In arXiv:1506.02175 it was described how one can obtain the Green-Schwarz superstring action from Yang-Mills theory on $\Sigma_2\times H^2$ while $H^2$ shrinks to a point. Here we also consider Yang-Mills theory on a three-dimensional manifold $\Sigma_2\times S^1$ and show that in the limit when the radius of $S^1$ tends to zero, the Yang-Mills action functional supplemented by a Wess-Zumino-type term becomes the Green-Schwarz superstring action.Comment: 11 pages, v3: clarifying remarks added, new section on embedding of the Green-Schwarz superstring into d=3 Yang-Mills theory include

FRT Construction for Dynamical Yang-Baxter Maps

Notions of an (H, X)-bialgebroid and of its dynamical representation are proposed. The dynamical representations of each (H, X)-bialgebroid form a tensor category. Every dynamical Yang-Baxter map R(lambda) satisfying suitable conditions, a generalization of the set-theoretical solution to the quantum Yang-Baxter equation, gives birth to an (H, X)-bialgebroid A_R. The categories of L-operators for R(lambda) and of dynamical representations of A_R are isomorphic as tensor categories

Loop groups in Yang-Mills theory

We consider the Yang-Mills equations with a matrix gauge group $G$ on the de Sitter dS$_4$, anti-de Sitter AdS$_4$ and Minkowski $R^{3,1}$ spaces. On all these spaces one can introduce a doubly warped metric in the form $d s^2 =-d u^2 + f^2 d v^2 +h^2 d s^2_{H^2}$, where $f$ and $h$ are the functions of $u$ and $d s^2_{H^2}$ is the metric on the two-dimensional hyperbolic space $H^2$. We show that in the adiabatic limit, when the metric on $H^2$ is scaled down, the Yang-Mills equations become the sigma-model equations describing harmonic maps from a two-dimensional manifold (dS$_2$, AdS$_2$ or $R^{1,1}$, respectively) into the based loop group $\Omega G=C^\infty (S^1, G)/G$ of smooth maps from the boundary circle $S^1=\partial H^2$ of $H^2$ into the gauge group $G$. From this correspondence and the implicit function theorem it follows that the moduli space of Yang-Mills theory with a gauge group $G$ in four dimensions is bijective to the moduli space of two-dimensional sigma model with $\Omega G$ as the target space. The sigma-model field equations can be reduced to equations of geodesics on $\Omega G$, solutions of which yield magnetic-type configurations of Yang-Mills fields. The group $\Omega G$ naturally acts on their moduli space.Comment: 8 pages; v3: clarifying remarks and references adde

Noncommutative QCD, first-order-in-theta-deformed instantons and 't Hooft vertices

For commutative Euclidean time, we study the existence of field configurations that {\it a)} are formal power series expansions in h\theta^{\m\n}, {\it b)} go to ordinary (anti-)instantons as h\theta^{\m\n}\to 0, and {\it c)} render stationary the classical action of Euclidean noncommutative SU(3) Yang-Mills theory. We show that the noncommutative (anti-)self-duality equations have no solutions of this type at any order in h\theta^{\m\n}. However, we obtain all the deformations --called first-order-in-$\theta$-deformed instantons-- of the ordinary instanton that, at first order in h\theta^{\m\n}, satisfy the equations of motion of Euclidean noncommutative SU(3) Yang-Mills theory. We analyze the quantum effects that these field configurations give rise to in noncommutative SU(3) with one, two and three nearly massless flavours and compute the corresponding 't Hooft vertices, also, at first order in h\theta^{\m\n}. Other issues analyzed in this paper are the existence at higher orders in h\theta^{\m\n} of topologically nontrivial solutions of the type mentioned above and the classification of the classical vacua of noncommutative SU(N) Yang-Mills theory that are power series in h\theta^{\m\n}.Comment: Latex. Some macros. No figures. 42 pages. Typos correcte

Penggunaan modul pembelajaran elektronik (MPE) pengenalan pelancongan H 111 : tinjauan terhadap pensyarah dan pelajar Diploma Pengurusan Pelancongan, Politeknik Johor Bahru

Era Teknologi Maklumat dan Komunikasi (ICT) telah melihat perkembangan penggunaan komputer sebagai alat berpotensi untuk meningkatkan proses pengajaran dan pembelajaran. Oleh itu, kajian ini meninjau Penggunaan Modul Pembelajaran Elektronik (MPE) dalam mata pelajaran Pengenalan Pelancongan H 111 di kalangan pensyarah dan pelajar semester satu Diploma Pengurusan Pelancongan, Politeknik Johor Bahru. Seramai 40 responden yang terdiri daripada pelajar dan tiga orang pensyarah telah dipilih bagi menjawab tiga persoalan kajian yang dinyatakan. Maklum balas melalui soal selidik pelajar telah dianalisis menggunakan perisian Sran'sf/caV Package /or <Sbc;'a/ Aaence (SPSS) versi 11.0, manakala maklum balas soalan terbuka pensyarah pula dipersembahkan dalam bentuk jadual serta penerangan. Dalam persoalan kajian pertama, skor min keseluruhan yang diperolehi terhadap penerimaan pelajar ke atas MPE Pengenalan Pelancongan H i l l yang dihasilkan adalah di tahap baik iaitu 3.74. Manakala persoaian kajian kedua, pelajar turut bersetuju bahawa isi kandungan MPE Pengenalan Pelancongan H i l l dapat meningkatkan tahap pemahaman mereka (skor min keseluruhan 3.654). Seterusnya dalam persoalan kajian ketiga, skor min keseluruhan yang diperolehi adalah 3.634 menunjukkan satu dapatan keputusan yang baik terhadap penggunaan MPE dalam membantu proses pembelajaran yang berkesan. Begitu juga dengan hasil dapatan yang diterima dari pensyarah, mendapati keputusan ketiga-tiga persoalan kajian berada di tahap setuju atau baik. Di akhir bab kajian ini, beberapa pandangan telah dikemukakan untuk mempertingkatkan lagi kecekapan MPE melalui pembangunan perisian yang lebih mantap di masa hadapan