We analytically compute correlation and response functions of scalar operators for the systems with Galilean and corresponding aging symmetries for general spatial dimensions d and dynamical exponent z, along with their logarithmic and logarithmic squared extensions, using the gauge/gravity duality. These non-conformal extensions of the aging geometry are marked by two dimensionful parameters, eigenvalue M of an internal coordinate and aging parameter α. We further perform systematic investigations on two-time response functions for general d and z, and identify the growth exponent as a function of the scaling dimensions δ of the dual field theory operators and aging parameter α in our theory. The initial growth exponent is only controlled by δ, while its late time behavior by α as well as δ. These behaviors are separated by a time scale order of the waiting time. We attempt to make contact our results with some field theoretical growth models, such as Kim-Kosterlitz model at higher number of spatial dimensions d.
Bibliographical noteFunding Information:
We thank to E. Kiritsis, Y.S. Myung, V. Niarchos for discussions and valuable comments on the higher dimensional KPZ class and the logarithmic extensions of CFT. S.H. is supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) with the grant number 2012046278 . S.H. and J.J. are supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) through the Center for Quantum Spacetime (CQUeST) of Sogang University with grant number 2005-0049409 . J.J. is supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) with the grant number 2010-0008359 . B.S.K. is grateful to the members of the Crete Center for Theoretical Physics, especially E. Kiritsis, for his warm hospitality during his visit. B.S.K. is supported in part by the Israel Science Foundation (grant number 1468/06 ).
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics