( 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

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 ( 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

Orientifold realization and its e ff ective description 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 of ON 0 type in the construction. Furthermore, there is a "resolved" proposal of this construction given in [2]. ON � ON 0 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 � . Ω γ := X h v, λ | ⌦ h v γ � 1 , λ | . (1) λ We have two Ω -background parameters q and t , and γ 2 = q 3 := t/q . In the 4d limit ( q ! 1 ) with γ = 1 , the above state can be shown to satisfy the boundary state condition, ( L n ⌦ 1) Ω γ =1 = ( L � n ⌦ 1) Ω γ =1 . (2)

As supportive evidence, we derive the qq-character (double quantized Seiberg-Witten curve) for this construction. We have the following results: • In the D 2 = SO(4) quiver, the qq-characters factorize into two SU(2)’s. • We have the same qq-characters for D 3 = SO(6) ' SU(4) as those in A 3 = SU(4). • In D 4 , we recover the generator of q - W -algebra [5] of D 4 type with qq-character of the vector representation of D 4 . 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 D 4 presented in [6].

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