We investigate a squashing deformation of 3d N=2 supersymmetric theories on three-sphere, which have four supercharges. The preserves SU(2)_L x U(1)_r isometry and all supersymmetries. compute the partition function find non-trivial dependence parameter. also consider large N limit certain class quiver gauge free energy order N^{3/2}, show that squashed sphere differs from round by factor depending only

We analyze the moduli space of low-energy limit 3-dimensional Maxwell-Chern-Simons theories described by circular quiver diagrams, as for 4-dimensional elliptic models. define using D3-NS5-(k,1)5-brane systems with an arbitrary number fivebranes. The supersymmetry is expected to be enhanced in limit. show that Higgs branch, which all bifundamental scalar fields develop vacuum expectation values, abelian orbifold ℂ4. confirm same geometry obtained M-theory dual brane system. also consider...

Abstract We study giant graviton expansions of the superconformal index 4D orbifold/orientifold theories. In general, a expansion is given as multiple sum over wrapping numbers. It known that can be reduced to simple for ${\cal N}=4$ U(N) supersymmetric Yang–Mills (SYM) by choosing appropriate variables. find such reduction occurs few examples orbifold and orientifold theories: $\mathbb {Z}_k$ orientifolds with O3 O7. also argue quiver gauge theory associated toric Calabi–Yau 3-fold...

We compute the index of 6d |$\mathcal {N}=(1,0)$| theories on |$\boldsymbol{S}^5\times \mathbb {R}$| containing vector and hypermultiplets. only consider perturbative sector without instantons. By compactifying |$\mathbb to |$\boldsymbol{S}^1$| with a twisted boundary condition taking small radius limit, we derive partition function squashed |$\boldsymbol{S}^5$|⁠. The 1-loop is represented in simple form triple sine function.

Abstract We investigate contributions of giant gravitons to the superconformal index. concentrate on coincident wrapped around a single cycle, and each contribution is obtained by certain variable change for fugacities from index worldvolume theory gravitons. Because we treat as series relates different convergence regions, need an analytic continuation before summing up such contributions. propose systematic prescription continuation. Although our argument based some unproven assumptions,...

A bstract Based on the D5-brane realization of Wilson line operators in anti-symmetric representations, we propose brane expansion formulas for I N,k , Schur index $$ \mathcal{N} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 U( N ) SYM decorated by representation rank k . For large ∞,k a double-sum expansion, and finite quadruple-sum expansion. Objects causing corrections are disk D3-branes ending D5-brane.

We calculate the Schur index of $\mathcal{N}=4$ $U(N)$ supersymmetric Yang-Mills theory with finite $N$ via AdS/CFT correspondence as contribution $\mathrm{D}3$-branes wrapped on contractible cycles in ${\mathbit{S}}^{5}$ some assumptions motivated by preliminary analyses. As far we have checked numerically it agrees calculated gauge side. In a certain limit reproduces analytic result given Bourdier, et al.

Abstract We propose a prescription to calculate the superconformal index of ${\cal N}=4$U(N) supersymmetric Yang–Mills theory with finite N on anti-de Sitter side. The finite-N corrections are included as contributions D3-branes wrapped around three-cycles in ${\boldsymbol S}^5$, which calculated gauge theories realized branes. single-wrapping contribution has been studied previous work, and we further confirm that inclusion multiple-wrapping correctly reproduces higher-order terms far have...

Abstract We discuss giant graviton expansions for the Schur index of ${\cal N}=4$ $U(N)$ SYM with insertion Wilson lines fundamental and antifundamental representations. first propose a double-sum expansion numerically confirm that it correctly reproduces line operator index. also find reduces to simple-sum when we treat as Taylor series respect specific fugacity.

We investigate a class of quiver Chern-Simons theories and their gravity duals. define the group fractional D3-brane charges in type IIB brane setup taking account creation due to Hanany-Witten effect, confirm that it agrees with 3-cycle homology dual geometry, which describes M2-branes, i.e., M5-branes wrapped on 3-cycles. The relation between charge torsion 3-form potential field is partially established. also discuss duality baryonic operators 5-cycles geometries. degeneracy conformal...

We construct supersymmetric theories on the SU(3)xU(1) symmetric squashed five-sphere with 2, 4, 6, and 12 supercharges. first determine Killing equation by dimensional reduction from 6d, use Noether procedure to actions. The Yang-Mills action is straightforwardly obtained Chern-Simons using a supersymmetry preserving constant vector multiplet.

Abstract We study the superconformal index of S-fold theories by using anti-de Sitter / conformal field theory correspondence. It is known that in large-$N$ limit reproduced as contribution bulk Kaluza–Klein modes. For finite-$N$, D3-branes wrapped around non-trivial cycle $\boldsymbol{S}^5/\mathbb{Z}_k$, which corresponds to Pfaffian-like operators, give corrections order $q^N$ index. calculate finite-$N$ analyzing fluctuations D3-branes. Comparisons results show our formula correctly...

We investigate finite-$N$ corrections to the superconformal indices of theories realized on M2- and M5-branes. For three-dimensional a stack $N$ M2-branes we calculate as contribution extended M5-branes in dual geometry $AdS_4\times \boldsymbol{S}^7$. take only M5-brane configurations with single wrapping into account, neglect multiple-wrapping configurations. compare results calculated from ABJM theory, find agreement up expected errors due multiple wrapping. six-dimensional by analyzing...

We investigate S^3/Z_n partition function of 3d N = 2 supersymmetric field theories. In a gauge theory the is sum contributions sectors specified by holonomies, and we should carefully choose relative signs among contributions. argue that factorization to holomorphic blocks useful criterion determine propose formula for them. show orbifold general non-gauge correctly factorized provided take appropriate signs. also present few examples point out sign factor closely related similar in lens...

A phase adjuster (PA) is proposed to improve the cooling effect of a loop-tube-type thermoacoustic system. PA device for accelerating particle velocity. The embedded in loop tube and narrows cross-sectional area part tube. creates strong boundary condition which velocity accelerated. It confirmed that phases sound pressure are adjusted so generated resonated with total length at one-wavelength resonance. This results great improvement

Monopole operators in Abelian 𝓝 = 4 Chern-Simons theories described by circular quiver diagrams are investigated. The magnetic charges of non-diagonal U(1) gauge symmetries form the SU(p) × SU(q) root lattice where p and q numbers untwisted twisted hypermultiplets, respectively. For monopole corresponding to vectors, we propose a correspondence between states wrapped M2-brane dual geometry.

We construct curved backgrounds with Euclidean signature admitting rigid supersymmetry by using a 5d $$ \mathcal{N} = 1 off-shell Poincaré supergravity. solve the conditions for background Weyl multiplet and vector multiplets that preserve at least one parameterized symplectic Majorana spinor, represent solution in terms of several independent fields. also show partition function does not depends on local degrees freedom Namely, as far we focus single coordinate patch, can freely change...