Classical Strings and Membranes in the AdS/CFT Correspondence
2015239 pages
Supervisors:
Thesis: PhD - Emmanuel Floratos(),
- Minos Axenides()
- Athens Natl. Capodistrian U.
URN/HDL:
Citations per year
Abstract:
In its strongest version, the AdS/CFT conjecture states that N = 4, su (Nc) super Yang-Mills (SYM)
theory is equal to type IIB string theory on AdS5 × S
5
. It is by far the most important equation of
contemporary theoretical physics, a sort of a "harmonic oscillator" for both the quantum theory of
gravity and gauge theories. It goes without saying that it is imperative to fully understand its limits
of validity and thoroughly investigate its implications. In particular, it would be desirable to solve
the theory, i.e. to be able to compute all of its observables.
One of the most important observables of AdS/CFT is its spectrum. According to the AdS/CFT
"dictionary", the spectrum of the theory comprises the energies of its string states, each of which
must be equal to the scaling dimensions of its dual gauge theory operator. The full spectral problem
of AdS/CFT is solved by integrability, in the sense that integrability provides the full set of algebraic
equations that determine it. Integrability methods are however severely limited in the regime of long,
strongly coupled operators, such as those that are dual to the Gubser-Klebanov-Polyakov (GKP)
strings, giant magnons and single spike strings.
In this thesis we study classical strings and branes in the context of the AdS/CFT correspondence.
Our goal is twofold: (1) develop methods for computing the AdS5/CFT4 spectrum in the case of long,
strongly coupled operators, by using classical strings and (2) understand the role of classical membranes
in AdS/CFT by investigating their stringy limits.
With regard to the first objective, we compute the classical spectra of long rotating GKP strings,
giant magnons and single spikes. The conserved linear and angular momenta of these string configurations,
that live either in AdS3 or R×S
2
, are known in parametric form in terms of the strings’ linear
and angular velocities. We eliminate the linear and angular velocities from the expressions that give
the energy of the strings, in favor of the strings’ conserved charges of linear and angular momenta.
This way, we find all the leading, subleading and next-to-next-to-leading terms in the dispersion relations
of the aforementioned string configurations. Our results are expressed in closed forms with
Lambert’s W-function.
For the second objective we introduce and study "stringy membranes", a new class of membranes
that live in AdS4/7 × S
7/4
or AdS4 × S
7
/Zk and have the same equations of motion, constraints and
conserved charges with strings that live in an appropriate subset of AdS5. Stringy membranes can
be constructed whenever the target spacetime contains a compact submanifold, by identifying one of
the submanifold’s compact coordinates with one of the membrane worldvolume coordinates. For the
stringy membranes that reproduce the pulsating and rotating GKP strings in AdS, we find that the
spectrum of their transverse quadratic fluctuations displays a multiple band/gap structure governed
by the Lamé equation. Conversely, string excitations are represented by a single-band/single-gap
Lamé pattern. These findings confirm the picture that we have of membranes as collective excitations
of some stringy counterparts.- AdS/CFT correspondence
- Superstrings
- Supermembranes
- Αντιστοιχία AdS/CFT
- ΥΠΕΡΧΟΡΔΕΣ
- Υπερμεμβράνες
- string: classical
- charge: conservation law
- magnon: giant
- string: excited state
References(386)
Figures(0)
- [1]
- [2]
- [3]
- [4]
- [5]
- [6]
- [7]
- [8]
- [9]
- [10]
- [11]
- [12]
- [13]
- [14]
- [15]
- [16]
- [17]
- [17]
- [18]
- [19]
- [20]
- [21]
- [22]
- [22]
- [23]