( N I C K ) RU I - D O N G Z H U D E PA R T M E N T O F P H YS I - - PowerPoint PPT Presentation

( N I C K ) RU I - D O N G Z H U

D E PA R T M E N T O F P H YS I C S U N I V E R S I T Y O F TO K YO

O R I E N T I F O L D R E A L I Z AT I O N O F D - T Y P E Q U I V E R G AU G E T H E O R I E S I N TO P O LO G I C A L V E R T E X F O R M A L I S M A N D B O U N DA RY S TAT E

Although the dual topological string construction is not known for D- type quiver gauge theories, their brane web construction was already given in [1]. In addition to (p, q) 5-branes, we also need orientifold

• f ON0 type in the construction. Furthermore, there is a "resolved"

proposal of this construction given in [2]. ON0 ON Our proposal for the computation of the partition function is to use the resolved diagram by assigning vertices in the usual way and a boundary state to the orientifold ON. Ωγ := X

λ

hv, λ| ⌦ hvγ1, λ| . (1) We have two Ω-background parameters q and t, and γ2 = q3 := t/q. In the 4d limit (q ! 1) with γ = 1, the above state can be shown to satisfy the boundary state condition, (Ln ⌦ 1)Ωγ=1 = (Ln ⌦ 1)Ωγ=1. (2)

Orientifold realization and its effective description

As supportive evidence, we derive the qq-character (double quantized Seiberg-Witten curve) for this construction.

We have the following results:

• In the D2 =SO(4) quiver, the qq-characters factorize into two

SU(2)’s.

• We have the same qq-characters for D3 =SO(6)'SU(4) as those

in A3 =SU(4).

• In D4, we recover the generator of q-W-algebra [5] of D4 type with

qq-character of the vector representation of D4. Triality among vector and two spinor representations is observed.

• We recover the derivative term which only appears in the double

quantized case in the qq-character of tensor representation of D4 presented in [6].

Poster no. 20, 3rd floor Thank you for your attention!