TY - JOUR

T1 - Generalized dynamical spin chain and 4-loop integrability in N = 6 superconformal Chern-Simons theory

AU - Bak, Dongsu

AU - Min, Hyunsoo

AU - Rey, Soo Jong

PY - 2010/3/11

Y1 - 2010/3/11

N2 - We revisit unitary representation of centrally extended psu (2 | 2) excitation superalgebra. We find most generally that 'pseudo-momentum', not lattice momentum, diagonalizes spin chain Hamiltonian and leads to generalized dynamic spin chain. All known results point to lattice momentum diagonalization for N = 4 super-Yang-Mills theory. Having different interacting structure, we ask if N = 6 superconformal Chern-Simons theory provides an example of pseudo-momentum diagonalization. For SO (6) sector, we study maximal shuffling and next-to-maximal shuffling terms in the dilatation operator and compare them with results expected from psu (2 | 2) superalgebra and integrability. At two loops, we rederive maximal shuffling term (3-site) and find perfect agreement with known results. At four loops, we first find absence of next-to-maximal shuffling term (4-site), in agreement with prediction based on integrability. We next extract maximal shuffling term (5-site), the most relevant term for checking the possibility of pseudo-momentum diagonalization. Curiously, we find that result agrees with integrability prediction based on lattice momentum, as in N = 4 super-Yang-Mills theory. Consistency of our results is fully ensured by checks of renormalizability up to six loops.

AB - We revisit unitary representation of centrally extended psu (2 | 2) excitation superalgebra. We find most generally that 'pseudo-momentum', not lattice momentum, diagonalizes spin chain Hamiltonian and leads to generalized dynamic spin chain. All known results point to lattice momentum diagonalization for N = 4 super-Yang-Mills theory. Having different interacting structure, we ask if N = 6 superconformal Chern-Simons theory provides an example of pseudo-momentum diagonalization. For SO (6) sector, we study maximal shuffling and next-to-maximal shuffling terms in the dilatation operator and compare them with results expected from psu (2 | 2) superalgebra and integrability. At two loops, we rederive maximal shuffling term (3-site) and find perfect agreement with known results. At four loops, we first find absence of next-to-maximal shuffling term (4-site), in agreement with prediction based on integrability. We next extract maximal shuffling term (5-site), the most relevant term for checking the possibility of pseudo-momentum diagonalization. Curiously, we find that result agrees with integrability prediction based on lattice momentum, as in N = 4 super-Yang-Mills theory. Consistency of our results is fully ensured by checks of renormalizability up to six loops.

UR - http://www.scopus.com/inward/record.url?scp=71849096204&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2009.10.011

DO - 10.1016/j.nuclphysb.2009.10.011

M3 - Article

AN - SCOPUS:71849096204

SN - 0550-3213

VL - 827

SP - 381

EP - 405

JO - Nuclear Physics B

JF - Nuclear Physics B

IS - 3

ER -