Basics on strings Flashcards
Relativistic strings are continuous and are therefore…
massless and travelling at the speed of light, perpendicular to the string, at the end points.
Embedded functions X, called ___, tell the place of the worldsheet in spacetime. They are maps from the world-sheet to some target space
string coordinates
What is the Nambu-Goto action?
The simplest string action functional
What is the condition for the orthogonality gauge?
The velocity is orthogonal to the string
What is the condition from the static gauge?
X0=c*tau
What constraint is imposed by the energy gauge?
Sigma at t=0
What three gauges (reparametrisation conditions) produces the wave equation from the Nambu-Goto action?
Static gauge, orthogonality gauge, energy gauge
String theory is a 2-dimensional ___ that generates an effective ___ in higher spacetime-dimensions.
QFT, QFT
Local symmetries concern the reparametrisation invariance and are determined by ____.
gauge choices
What symmetries concern the Poincaré symmetric target space
Global symmetries
How is the Regge slope parameter defined?
alpha’=hbar*E^2/J
How is the string length defined?
ls=hbarcsqrt(alpha’)
Why do we use the light-cone gauge?
To avoid quantisation problems from the fact that the functions (string coordinates) are bilinear (having two arguments)
Are the light-cone coordinates Lorentz invariant?
No
Only for ____ are the only physical motions perpendicular to the string
relativistic strings
Why are relativistic strings sometimes referre to as massless strings?
Because the mass (or rest energy) arises only because the string has a tension
What is the dimension of tau and sigma in the light-cone gauge?
They are dimensionless
Are there any dimensionless, adjustable parameters in string theory?
No, there aren’t
How is the effective string mass defined?
mu_eff=gamma*T_0/c^2
These previous gauges simplify enormously but we still have quadratic constraints (the functions are bilinear - they have ___). To avoid quantisation problems we will simplify this by using ___.
two arguments, light-cone coordinates
In the light cone gauge, tau is proportional to
X^+
From the mode expansion (of the light-cone solutions) we define ____ as half the sum of all the renormalised creation and annihiliation operation products.
the transverse Virasoro generators
The ambiguities (such as D and a) produced when defining the quantum theory are fixed (D becoming the critical dimension) by requiring that ___
the theory be Lorentz invariant
What is beta for closed strings?
Beta=1
Except for shared position and momentum zero modes, the operator content of ____ can be viewed as two commuting copies of the open string operators.
quantum closed strings
Where does the level matching condition for closed strings come from?
From alpha_0^-=alphabar_0^- which leads to L_0^perp=Lbar_0^perp
___ controls the strength of string interactions.
The dilaton state (this exists in closed string theory)
Imposing ___ on closed strings creates two sectors: untwisted (invariant) and twisted (antiperiodic and expressed in half integers: tachyons but no massless fields) closed strings.
Z_2 identification
The closed string coupling constant, which is also
the loop counting parameter, comes from ___
the dilaton
Two problems with bosonic strings: ___ → unstable, and no spacetime ___. This is solved by adding a fermionic field. If we make these spinors we find the NSR formalism.
tachyon, fermions
Superstring theory is space-time supersymmetric, tachyon free, and describes all known massless bosonic and fermionic particles. It is an extension to the ___. The bosonic string coordinates are accompanied by the fermionic coordinates that can be divided into two sectors. The Ramond (Naveu-Schwarz) sector concerns periodic (antiperiodic) boundary conditions and sum over integer (half-integer) modes.
Poincaré algebra
From ___ it follows that D=10 for superstrings.
the spacetime Lorentz commutator
In the __ sector the space of states transform as spinor representations of SO(8) and we have 8 (fermionic) zero modes. These create 8 ground states with an even number of creation operators (and 8 with odd). These are left and right chiral spinors. They have opposite spin statistic properties.
Ramond
This spin statistic (and number counting) problem is solved with the __ which keeps only the left chiral ground states and fermionic states so that R becomes R-. Similarly the NS sector becomes the NS+ sector as the tachyon is eliminated so that only bosonic integer spin fields are left.
GSO projection
What type of states are contained in the R sector?
fermionic states
The closed superstring has left and right going modes (NS+,NS+), (NS+, R-), (R,NS+), (R,R-) where the tachyon is omitted, the middle two are the ____ fields (spin 3/2 anti-commuting fields for local supersymmetry needed for supergravity).
Rarita-Schwinger
Is the NS-sector periodic?
No, it’s antiperiodic
Type IIB theory contains two scalar fields, the scalar φ(x) and the pseudo-scalar A(x). They
appear in the Lagrangian together as a ___, i.e., these two fields
can be viewed as coordinates on the coset space SU(1, 1)/U(1) (which is an unbounded
Euclidean hyperbolic space familiar from the course in GR).
non-linear sigma-model
Type I supergravity theory is obtained from the type
IIB theory by imposing ___ on the closed string.
invariance under orientation reversal
