String Field Theory - Witten's Cubic Open String Field Theory

Witten's Cubic Open String Field Theory

The best studied and simplest of covariant interacting string field theories was constructed by Edward Witten. It describes the dynamics of bosonic open strings and is given by adding to the free open string action a cubic vertex:

,

where, as in the free case, is a ghostnumber one element of the BRST-quantized free bosonic open-string Fock-space.

The cubic vertex,

is a triliniar map which takes three string fields of total ghostnumber three and yields a number. Following Witten, who was motivated by ideas from noncommutative geometry, it is conventional to introduce the -product defined implicitly through

The -product and cubic vertex satisfy a number of important properties (allowing the to be general ghost number fields):

  1. Cyclicity :
  2. BRST invariance :
    For the -product, this implies that acts as a graded derivation
  3. Associativity
    In terms of the cubic vertex,

In these equations, denotes the ghost number of .

Read more about this topic:  String Field Theory

Famous quotes containing the words cubic, open, string, field and/or theory:

    “One of the great natural phenomena is the way in which a tube of toothpaste suddenly empties itself when it hears that you are planning a trip, so that when you come to pack it is just a twisted shell of its former self, with not even a cubic millimeter left to be squeezed out.”
    —Robert Benchley (1889–1945)

    “I rarely speak about God. To God, yes. I protest against Him. I shout at Him. But to open a discourse about the qualities of God, about the problems that God imposes, theodicy, no. And yet He is there, in silence, in filigree.”
    —Elie Wiesel (b. 1928)

    “The Indian remarked as before, “Must have hard wood to cook moose-meat,” as if that were a maxim, and proceeded to get it. My companion cooked some in California fashion, winding a long string of the meat round a stick and slowly turning it in his hand before the fire. It was very good. But the Indian, not approving of the mode, or because he was not allowed to cook it his own way, would not taste it.”
    —Henry David Thoreau (1817–1862)

    “She is as in a field a silken tent
    At midday when a sunny summer breeze
    Has dried the dew and all its ropes relent,”
    —Robert Frost (1874–1963)

    “No one thinks anything silly is suitable when they are an adolescent. Such an enormous share of their own behavior is silly that they lose all proper perspective on silliness, like a baker who is nauseated by the sight of his own eclairs. This provides another good argument for the emerging theory that the best use of cryogenics is to freeze all human beings when they are between the ages of twelve and nineteen.”
    —Anna Quindlen (20th century)