Developments Flashcards
What is a modulus?
A free parameter (=it lives in a dimension without any potential). Moduli span moduli space.
What is the Einstein-Hilbert action?
The action that yields the Einstein field equations from Hamilton’s principle. S=1/2\kappa \int R \sqrt {-g}d^4x,
Electric fields appear as ___ in the dual world.
boosts
Magnetic fields appear as ____ in the dual world
rotations
To obtain the constraints on covariant strings we must impose that…
… the stress energy tensor is zero as an operator
What fixes the dimensionality in Polyakov formalism?
The ghost (b,c) field.
AdS/CFT correspondence suggests that it is possible to describe a force in quantum mechanics (like electromagnetism, the weak force or the strong force) in a certain number of dimensions (for example four) with a string theory where the strings exist in an anti-de Sitter space, with ____.
one additional (non-compact) dimension
What is the fancy name for local scale invariance?
Weyl invariance. This holds for two-dimensional conformal field theory describing the world sheet of a string
The Polyakov string action is classically equivalent to ___
the Nambu-Goto string action
Just like for transverese Virasoro operators in the light-cone gauge, all positively moded Virasoro operators must… (about physical states)
annihilate physical states. (Physical states must be admissable (being primaries (annihilated by all positively moded Virasoro operators) and annihilated by L_0-1), and not a descendent (linear products of negatively moded Virasoro opertators)
Physical states (h=1) fulfill two conditions, which?
- It is admissable (L_n+\delta_n,0)|state>=0 n>=0
2. It is NOT a descendent (a linear product of negatively moded Virasoro operators)
Admissible states are both ___ and ___.
primaries, annihilated by L_0-1
The Polyakov string is made conformal (Weyl) invariant through introducing ___ in the Faddeev-Popov procedure. This sets D to 26. Then, a is set to -1 since the gauge invariance in the low energy field theory only works if D=26 and a=-1.
anti-commuting ghost fields
What is a genus?
A genus g is the number of holes in any two-dimensional surface without boundaries. The Euler number Chi=2-2g.
How is the Euler number defined?
Chi=2-2g.
For the Polyakov action to include supergravity the Lagrangian has to produce the ____. This is the relativistic field equation of spin-3/2 fermions. It is similar to the Dirac equation for spin-1/2 fermions.
Rarita-Schwinger equation
Massless vector fields become massive (Higgs mechanism) when ____
D-branes move away
A Dp-brane has a ___ living on its world-volume, and a ___ for each normal direction.
Maxwell field, massless scalar
How many directions have at least one Neumann endpoint condition on a Dp-branes?
p
When are the Robin boundary conditions applicable?
When considering a D-brane with electromagnetic field.
Born-Infeld theory solves the ___ problem in electrodynamics
infinite self-energy
What is the Swampland program?
An aim to extract physics from quantum gravity by finding conditions (so called conjectures). Some examples are: gravity is the weakest force, there are no global symmetries, there are no stable (or semi-stable) de Sitter solutions at all.
