PT-symmetric interpretation of double scaling

TY - JOUR

T1 - PT-symmetric interpretation of double scaling

AU - Moshe, Moshe

AU - Bender, Carl

AU - Sarkar, Sarben

PY - 2013/3/15

Y1 - 2013/3/15

N2 - The conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the Lagrangian defines a quantum theory with an upside-down potential whose energy appears to be unbounded below. Worse yet, the integral representation of the partition function of the theory does not exist. It is shown that one can avoid these difficulties if one replaces the original theory by its -symmetric analog. For a zero-dimensional O(N)-symmetric quartic vector model the partition function of the -symmetric analog is calculated explicitly in the double-scaling limit.

AB - The conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the Lagrangian defines a quantum theory with an upside-down potential whose energy appears to be unbounded below. Worse yet, the integral representation of the partition function of the theory does not exist. It is shown that one can avoid these difficulties if one replaces the original theory by its -symmetric analog. For a zero-dimensional O(N)-symmetric quartic vector model the partition function of the -symmetric analog is calculated explicitly in the double-scaling limit.

U2 - 10.1088/1751-8113/46/10/102002

DO - 10.1088/1751-8113/46/10/102002

M3 - Article

SN - 1751-8113

VL - 46

JO - Journal Of Physics A-Mathematical And Theoretical

JF - Journal Of Physics A-Mathematical And Theoretical

IS - 10

M1 - 102002

ER -