We consider an exotic baryon (pentaquark) as a bound state of two-body systems composed of a baryon (nucleon) and a meson. We used a baryon-meson picture to reduce a complicated five-body problem to simple two-body problems. The homogeneous Lippmann-Schwinger integral equation is solved in configuration space by using one-pion exchange potential. We calculate the masses of pentaquarks <math id="M1"><msub><mrow><mi>θ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>u</mi><mi>u</mi><mi>d</mi><mi>d</mi><mover><mrow><mi>c</mi></mrow><mo>¯</mo></mover><mo>)</mo></math> and <math id="M2"><msub><mrow><mi>θ</mi></mrow><mrow><mi>b</mi></mrow></msub><mo>(</mo><mi>u</mi><mi>u</mi><mi>d</mi><mi>d</mi><mover><mrow><mi>b</mi></mrow><mo>¯</mo></mover><mo>)</mo></math>.

Iran

N. Tazimi

M. Monemzadeh

Sh. Babaghodrat

Calculating Masses of Pentaquarks Composed of Baryons and Mesons

In the context of 4D/2D dualities, SH c algebra, introduced by Schiffmann and Vasserot, provides a systematic method to analyse the instanton partition functions of N = 2 $$ \mathcal{N}=2 $$ supersymmetricgaugetheories. Inthispaper,werewritetheSH c algebrainterms of three holomorphic fields D 0 ( z ), D ±1 ( z ) with which the algebra and its representations are simplified. The instanton partition functions for arbitrary N = 2 $$ \mathcal{N}=2 $$ super Yang-Mills theories with A n and A n (1) type quiver diagrams are compactly expressed as a product of four building blocks, Gaiotto state, dilatation, flavor vertex operator and intertwiner which are written in terms of SH c and the orthogonal basis introduced by Alba, Fateev, Litvinov and Tarnopolskiy. These building blocks are characterized by new conditions which generalize the known ones on the Gaiotto state and the Carlsson-Okounkov vertex. Consistency conditions of the inner product give algebraic relations for the chiral ring generating functions defined by Nekrasov, Pestun and Shatashvili. In particular we show the polynomiality of the qq-characters which have been introduced as a deformation of the Yangian characters. These relations define a second quantization of the Seiberg-Witten geometry, and, accordingly, reduce to a Baxter TQ-equation in the Nekrasov-Shatashvili limit of the Omega-background.

Italy

Jean-Emile Bourgine

Japan

Yutaka Matsuo

South Korea

Hong Zhang

Holomorphic field realization of SH c and quantum geometry of quiver gauge theories

Recently an orthogonal basis of W N $$ {\mathcal{W}}_N $$ -algebra (AFLT basis) labeled by N -tuple Young diagrams was found in the context of 4D/2D duality. Recursion relations among the basis are summarized in the form of an algebra SH c which is universal for any N . We show that it has an S 3 $$ {\mathfrak{S}}_3 $$ automorphism which is referred to as triality. We study the level-rank duality between minimal models, which is a special example of the automorphism. It is shown that the nonvanishing states in both systems are described by N or M Young diagrams with the rows of boxes appropriately shuffled. The reshuffling of rows implies there exists partial ordering of the set which labels them. For the simplest example, one can compute the partition functions for the partially ordered set (poset) explicitly, which reproduces the Rogers-Ramanujan identities. We also study the description of minimal models by SH c . Simple analysis reproduces some known properties of minimal models, the structure of singular vectors and the N -Burge condition in the Hilbert space.