A tail of a quark in 𝒩 = 4 SYM

Abstract

We study the dynamics of a 'composite' or 'dressed' quark in stronglycoupled large-N c N = 4 super-Yang-Mills, making use of the AdS/CFT correspondence. We show that the standard string dynamics nicely captures the physics of the quark and its surrounding non-Abelian field configuration, making it possible to derive a relativistic equation of motion that incorporates the effects of radiation damping. From this equation one can deduce a non-standard dispersion relation for the composite quark, as well as a Lorentz covariant formula for its rate of radiation. We explore the consequences of the equation in a few simple examples.

Branes from light: embeddings and energetics for symmetric k-quarks in N = 4 $$ \mathcal{N}=4 $$ SYM

“…We start in Section 2 by reviewing Mikhailov's embedding (19) for the string. Whereas the emphasis in many of the early applications (see, e.g., [12,35,36]) was on the reliance of his construction on null geodesics on the string worldsheet, which are only known after the embedding has been specified, we observe here that these curves turn out to also be null geodesics directly in spacetime (see also [20]). This implies that Mikhailov's solution can be constructed by shooting light rays in from the AdS boundary.…”

“…from which the second term drops out because n · v = 0. In more detail, at some initial time τ 0 we apply the boost (35) to define n µ (τ 0 , θ, φ) = Λ µ ν n µ R (θ, φ), and then evolve from there using (36) to obtain n µ at arbitrary times. Note that the result generally depends on the probe's velocity and acceleration.…”

Zero temperature dissipation and holography

“…One of the interesting results is that there is a drag force (dissipating energy) on the fluctuating external quark even at zero temperature. This was identified as being due to radiation [10][11][12][13][14][15][16][17][18][19][20][21]. This force term in the Langevin equation was of the form…”

Holographic Brownian motion at finite density

“…It is known from classical electrodynamics that the energy loss 6 due to radiation is proportional to square of the acceleration (a). See [10,[26][27][28][29][30][31][32][33][34][35][36][37] for related works.…”