On the quantization of Seiberg-Witten geometry

We propose a double quantization of four-dimensional $$ \mathcal{N} $$ N = 2 Seiberg-Witten geometry, for all classical gauge groups and a wide variety of matter content. This can be understood as a set of certain non-perturbative Schwinger-Dyson identities, following the program initiated by Nekrasov [1]. The construction relies on the computation of the instanton partition function of the gauge theory on the so-called Ω-background on ℝ4, in the presence of half-BPS codimension 4 defects. The two quantization parameters are identified as the two parameters of this background. The Seiberg-Witten curve of each theory is recovered in the flat space limit. Whenever possible, we motivate our construction from type IIA string theory.

Quantum geometry and θ-angle in five-dimensional super Yang-Mills

Five-dimensional Sp(N) supersymmetric Yang-Mills admits a ℤ2 version of a theta angle θ. In this note, we derive a double quantization of the Seiberg-Witten geometry of $$ \mathcal{N} $$ N = 1 Sp(1) gauge theory at θ = π, on the manifold S1× ℝ4. Crucially, ℝ4 is placed on the Ω-background, which provides the two parameters to quantize the geometry. Physically, we are counting instantons in the presence of a 1/2-BPS fundamental Wilson loop, both of which are wrapping S1. Mathematically, this amounts to proving the regularity of a qq-character for the spin-1/2 representation of the quantum affine algebra $$ {U}_q\left(\hat{A_1}\right) $$ U q A 1 ̂ , with a certain twist due to the θ-angle. We motivate these results from two distinct string theory pictures. First, in a (p, q)-web setup in type IIB, where the loop is characterized by a D3 brane. Second, in a type I′ string setup, where the loop is characterized by a D4 brane subject to an orientifold projection. We comment on the generalizations to the higher rank case Sp(N) when N > 1, and the SU(N) theory at Chern-Simons level κ when N > 2.

Blind Detection of Tampered JPEG Image Based on Blocking Artifacts of Double Quantization

In this paper, a novel approach is proposed to detect JPEG image forgery based on the inconsistencies of quantization tables. The primary quantization table of tempered image is firstly estimated. Then the blocking artifact measure (BAM) of each 8×8 DCT coefficient block is computed using the estimated quantization matrix, and the BAMs of all blocks are sorted in descending order. Select a certain number of blocks of which the BAM is in the front of the order. Labeling the connected components of blocks in order to eliminate some abnormal blocks and gain the connected doctored blocks. Experimental results demonstrate the validity of the proposed approach.