Discrete gravitational dimensions

被引:55
作者
Arkani-Hamed, N [1 ]
Schwartz, MD [1 ]
机构
[1] Harvard Univ, Jefferson Phys Lab, Cambridge, MA 02138 USA
来源
PHYSICAL REVIEW D | 2004年 / 69卷 / 10期
关键词
D O I
10.1103/PhysRevD.69.104001
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
We study the physics of a single discrete gravitational extra dimension using the effective field theory for massive gravitons. We first consider a minimal discretization with 4D gravitons on the sites and nearest neighbor hopping terms. At the linear level, 5D continuum physics is recovered correctly, but at the nonlinear level the theory becomes highly nonlocal in the discrete dimension. There is a peculiar UV/IR connection, where the scale of strong interactions at high energies is related to the radius of the dimension. These new effects formally vanish in the limit of zero lattice spacing, but do not do so quickly enough to reproduce the continuum physics consistently in an effective field theory up to the 5D Planck scale. Nevertheless, this model does make sense as an effective theory up to energies parametrically higher than the compactification scale. In order to have a discrete theory that appears local in the continuum limit, the lattice action must have interactions between distant sites. We speculate on the relevance of these observations to the construction of finite discrete theories of gravity in four dimensions.
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页数:5
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共 12 条
[1]   (De)constructing dimensions and non-commutative geometry [J].
Alishahiha, M .
PHYSICS LETTERS B, 2001, 517 (3-4) :406-414
[2]   Effective field theory for massive gravitons and gravity in theory space [J].
Arkani-Hamed, N ;
Georgi, H ;
Schwartz, MD .
ANNALS OF PHYSICS, 2003, 305 (02) :96-118
[3]   (De)constructing dimensions [J].
Arkani-Hamed, N ;
Cohen, AG ;
Georgi, H .
PHYSICAL REVIEW LETTERS, 2001, 86 (21) :4757-4761
[4]   Gravity in dynamically generated dimensions [J].
Bander, M .
PHYSICAL REVIEW D, 2001, 64 (10)
[5]   Effective Lagrangians and universality classes of nonlinear bigravity [J].
Damour, T ;
Kogan, II .
PHYSICAL REVIEW D, 2002, 66 (10)
[6]   CONSISTENT INTERACTING MASSIVE SPIN-2 REQUIRES AN INFINITY OF STATES [J].
DUFF, MJ ;
POPE, CN ;
STELLE, KS .
PHYSICS LETTERS B, 1989, 223 (3-4) :386-390
[7]   On relativistic wave equations for particles of arbitrary spin in an electromagnetic field [J].
Fierz, M ;
Pauli, W .
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1939, 173 (A953) :0211-0232
[8]   Gauge invariant effective Lagrangian for Kaluza-Klein modes [J].
Hill, CT ;
Pokorski, S ;
Wang, J .
PHYSICAL REVIEW D, 2001, 64 (10)
[9]   The cosmological constant and the deconstruction of gravity [J].
Jejjala, V ;
Leigh, RG ;
Minic, D .
PHYSICS LETTERS B, 2003, 556 (1-2) :71-79
[10]   Multi-graviton theory, a latticized dimension and the cosmological constant [J].
Kan, N ;
Shiraishi, K .
CLASSICAL AND QUANTUM GRAVITY, 2003, 20 (23) :4965-4971