D-brane solutions in pp-wave background

Abstract

We present classical solutions for a D5 and NS5-branes in a pp-wave background. The worldvolume coordinates for these branes lie along a six dimensional pp-wave configuration obtained from AdS 3 × S 3 in a Penrose limit. One in addition has nontrivial R-R 3-form field strength as well as a dilaton background. Classical solutions for Dp-branes (p > 5), as well as their bound states, are then generated in both IIA and IIB string theories by using T -duality symmetries. We also briefly discuss the construction of Dp-branes in ppwave backgrounds, obtained from string theories on AdS m ×S m . Finally, the construction of the above D5-brane solution is presented from the point of view of the Green-Schwarz worldsheet string theory and its low lying spectrum is discussed.String theory in the presence of pp-wave backgrounds [1][2][3][4][5][6][7] has generated lots of excitement among physicists searching for a deep connection between quatum gravity and gauge theory dynamics. Such string backgrounds are technically tractable, and have direct applications to the four dimensional conformal theories from the point of view of a duality between string and gauge theories. The fact that pp-waves provide exact solutions of string theory, including in the presence of R − R fields [4], is now known for long time. It has now been realized [8,9] that in some special cases, they give rise to exactly solvable string theory with a quadratic action. As a result the spectrum of the theory can be explicitly obtained. Moreover, an interesting connection of pp-wave background with gauge field theories emerges by realizing that they can be obtained [10]

Thermal amplitudes in DLCQ superstrings on pp-waves

“…The Gaussian path-integral is easily evaluated and gives the determinant of the Klein-Gordon operator −4∂ z ∂z + m 2 . Working with the coordinates z = ξ 1 + τ ξ 2 ,z = ξ 1 +τ ξ 2 and making use of (2.27), we can show 34) up to a divergent factor that is independent of τ ,τ , m and should be regulated. It manifestly reproduces the modular transformation formulas (2.33).…”

“…We shall only focus on the D-branes in the maximally supersymmetric 10-dimensional pp-wave [32,33,24], although the generalization to more general backgrounds (say, the 6-dimensional pp-waves analyzed in the next section) is straightforward (see the papers [34]). …”

“…The check of level matching condition is only the non-trivial task. In fact, in the expression of (4.33) the summation over q acts as the projection operator 34) which ensures the correct level matching condition (4.20).…”

Strings in plane wave backgrounds

“…[115,116,117]). I will summarize these results below, overviews over many aspects on D-branes on the plane wave can be found in [118,119].…”

pp-wave/Yang–Mills correspondence: an explicit check

“…Integration over the eight transverse directions becomes a simple Gaussian integral which pro- 33) where…”