hamiltonian index
Recently Published Documents


TOTAL DOCUMENTS

20
(FIVE YEARS 2)

H-INDEX

5
(FIVE YEARS 0)

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Arash Arabi Ardehali ◽  
Sameer Murthy

Abstract We consider the S3×S1 superconformal index ℐ(τ) of 4d $$ \mathcal{N} $$ N = 1 gauge theories. The Hamiltonian index is defined in a standard manner as the Witten index with a chemical potential τ coupled to a combination of angular momenta on S3 and the U(1) R-charge. We develop the all-order asymptotic expansion of the index as q = e2πiτ approaches a root of unity, i.e. as $$ \overset{\sim }{\tau } $$ τ ~ ≡ mτ+n → 0, with m, n relatively prime integers. The asymptotic expansion of log ℐ(τ) has terms of the form $$ \overset{\sim }{\tau } $$ τ ~ k, k = −2, −1, 0, 1. We determine the coefficients of the k = −2, −1, 1 terms from the gauge theory data, and provide evidence that the k = 0 term is determined by the Chern-Simons partition function on S3/ℤm. We explain these findings from the point of view of the 3d theory obtained by reducing the 4d gauge theory on the S1. The supersymmetric functional integral of the 3d theory takes the form of a matrix integral over the dynamical 3d fields, with an effective action given by supersymmetrized Chern-Simons couplings of background and dynamical gauge fields. The singular terms in the $$ \overset{\sim }{\tau } $$ τ ~ → 0 expansion (dictating the growth of the 4d index) are governed by the background Chern-Simons couplings. The constant term has a background piece as well as a piece given by the localized functional integral over the dynamical 3d gauge multiplet. The linear term arises from the supersymmetric Casimir energy factor needed to go between the functional integral and the Hamiltonian index.


2021 ◽  
Vol 36 (3) ◽  
pp. 403-411
Author(s):  
Ze-meng Liu ◽  
Li-ming Xiong

AbstractIn this note, we show a sharp lower bound of $$\min \left\{{\sum\nolimits_{i = 1}^k {{d_G}({u_i}):{u_1}{u_2} \ldots {u_k}}} \right.$$ min { ∑ i = 1 k d G ( u i ) : u 1 u 2 … u k is a path of (2-)connected G on its order such that (k-1)-iterated line graphs Lk−1(G) are hamiltonian.


2020 ◽  
Vol 343 (6) ◽  
pp. 111841
Author(s):  
Xia Liu ◽  
Liming Xiong

2011 ◽  
Vol 159 (4) ◽  
pp. 246-250 ◽  
Author(s):  
Zdeněk Ryjáček ◽  
Gerhard J. Woeginger ◽  
Liming Xiong

2010 ◽  
Vol 310 (15-16) ◽  
pp. 2082-2090 ◽  
Author(s):  
Longsheng Han ◽  
Hong-Jian Lai ◽  
Liming Xiong ◽  
Huiya Yan

2009 ◽  
Vol 309 (9) ◽  
pp. 2798-2807
Author(s):  
Přemysl Holub ◽  
Liming Xiong

2009 ◽  
Vol 309 (1) ◽  
pp. 288-292 ◽  
Author(s):  
Yi Hong ◽  
Jian-Liang Lin ◽  
Zhi-Sui Tao ◽  
Zhi-Hong Chen
Keyword(s):  

2008 ◽  
Vol 308 (24) ◽  
pp. 6373-6382 ◽  
Author(s):  
Liming Xiong ◽  
Qiuxin Wu

2008 ◽  
Vol 308 (20) ◽  
pp. 4779-4785 ◽  
Author(s):  
Zhang Lili ◽  
Elaine Eschen ◽  
Hong-Jian Lai ◽  
Yehong Shao
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document