By Ammon, Martin; Erdmenger, Johanna
Gauge/gravity duality creates new hyperlinks among quantum idea and gravity. It has ended in new strategies in arithmetic and physics, and offers new instruments to unravel difficulties in lots of components of theoretical physics. This e-book is the 1st textbook in this very important subject, allowing graduate scholars and researchers in string idea and particle, nuclear and condensed topic physics to get accustomed to the topic. concentrating on the basic features in addition to at the functions, this textbook courses readers via a radical clarification of the relevant strategies of gauge/gravity duality. For the AdS/CFT correspondence, it explains intimately how string concept presents the conjectured map. Generalisations to much less symmetric circumstances of gauge/gravity duality and their purposes are then offered, specifically to finite temperature and density, hydrodynamics, QCD-like theories, the quark-gluon plasma and condensed subject platforms. The textbook incorporates a huge variety of routines, with suggestions to be had on-line at www.cambridge.org/9781107010345
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Extra info for Gauge/gravity duality : foundations and applications
89) is implicitly assumed and the kinetic term reads ∂φ ∂τ ∂ μ φ∂μ φ = 2 + (∇φ)2 . 90) In the Euclidean version of the path integral, the weight factor e−SE is strongly damped and positive definite. 88), are more obvious. Since the weight factor e−SE is positive definite and therefore can be normalized to one, we may think of it as a density matrix. This connection can be made more precise. 91) n where the set of states |n forms a basis of the Hilbert space. 45). For the partition function we thus have to sum over all transition amplitudes with φi = φf .
128) |k|< and the Wilsonian effective action SEeff [φ; ] is determined by e−SE eff [φ; ] = Dφ |k|> e−SE [φ] . 129) For φ 4 theory, the Wilsonian effective action SEeff [φ; ] is given by an effective Lagrangian in position space expressed as an expansion in local operators, Leff E = Z( ) m2 ( ) 2 g( ) 4 ∂μ φ∂ μ φ + φ + φ +O 2 2 4! 130) where Z(λ), m2 ( ) and g( ) are all finite functions of . 130) represents higher order terms such as φ 2n with n ≥ 3 or terms including derivatives. 127) by inducing interactions among the remaining Fourier modes φ(k), which previously were mediated by fluctuations of the large-k modes.
203 on Sat Jun 20 19:55:31 BST 2015. 5 Regularisation and renormalisation The derivatives are to be taken for fixed bare parameters. 112) is the renormalisation group equation or RG equation. γ is the anomalous dimension of the field φ, while γm is the anomalous dimension of the mass parameter m. Note the similarity between the definitions of γm and β. From now on, we view the mass as a generalised coupling constant. 110). 84) satisfies ∂ ∂ ∂ δ μ +β + mγm − γ d d x ϕ(x) [ϕ, m, g, μ] = 0. 113), determine β, γm and γ to first non-trivial order in g for φ 4 theory.
Gauge/gravity duality : foundations and applications by Ammon, Martin; Erdmenger, Johanna