IIB Soliton Spectra with All Fluxes Activated

TL;DR

This work addresses the absence of a fully S-duality covariant charge classification in type IIB string theory and proposes a generalized AHSS-like framework to compute conserved RR and NS charges, conjectured to form a K-theory of dual pairs. It tests the approach by applying the Maldacena–Moore–Seiberg framework to branes on $S^3$ with both NS and RR fluxes and comparing the results to the baryon spectrum in $AdS^5\times \mathbf{RP}^5$, finding consistency in the predicted spectra and their dependence on flux quanta. The analysis reveals that charge groups can change under Brown–Teitelboim–like phase transitions, highlighting the need for a dynamic, flux-aware extension of K-theory and its extension maps. The paper also explores dielectric D9-branes and speculates about a K-theory of dual pairs that may refine conventional K-theory by encoding dual gauge data, outlining concrete directions for a complete, duality-consistent classification of IIB solitons.

Abstract

Building upon an earlier proposal for the classification of fluxes, a sequence is proposed which generalizes the AHSS by computing type IIB string theory's group of conserved RR and also NS charges, which is conjectured to be a K-theory of dual pairs. As a test, the formalism of Maldacena, Moore and Seiberg (hep-th/0108100) is applied to classify D-branes, NS5-branes, F-strings and their dielectric counterparts in IIB compactified on a 3-sphere with both NS and RR background fluxes. The soliton spectra on the 3-sphere are then compared with the output of the sequence, as is the baryon spectrum in Witten's non-spin^c example, AdS^5xRP^5. The group of conserved charges is seen to change during Brown-Teitelboim-like phase transitions which change the effective cosmological constant.

Figures (7)

• Figure 1: $k$ branes which each intersect an $S^3$ at a point carry the same charge as one brane which intersects an $S^3$ at a manifold $\Sigma$ if the integral of the first Chern class of its gauge bundle over $\Sigma$ is equal to $k$. A paralell to the Kondo model indicates FS that not only do these two configurations carry the same charges, but also that there are dynamical processes which interpolate between them.
• Figure 2: A D3-brane wraps a 3-sphere with $k$ units of $H$-flux and no $G_3$ flux. It also extends in a spacelike direction which is not shown. The vertical direction of the diagram is timelike and at each moment in time a crosssection $\Sigma$ of the $S^3$ is chosen on which the D3 is wrapped. As $\Sigma$ shrinks to a point if we use the gauge choice which keeps $B$ finite then $\int_\Sigma F=6\pi$ and so the D3 cannot decay entirely. Instead it decays to 4 D-strings and 1 anti D-string. A D-string and an anti D-string annihilate, leaving 3 D-strings. Thus D-string number is only conserved modulo $3$ while F-string number is conserved completely.
• Figure 3: One instant in the life of a D3-brane (vertex) wrapping a 3-sphere with $k=9$ units of $H$-flux and $j=12$ of $G_3$ flux. It also extends in a timelike direction which is not shown. The induced gauge theory fluxes cannot exist on a compact space and so the D3 must have a noncompact worldvolume. In this picture it has noncompact tendrils with string charges. In a ground state in flat space there will be $3=gcd(9,12)$ tendrils each of which carries $(3,4)$-string charge. The width of a tendril is inversely proportional to its distance from the vertex HanWit, and so these strings are always slightly dielectric.
• Figure 4: A D5-brane wraps the $S^3$, a contractible 2-cycle $\Sigma$ and some other irrelevant direction. The integral of the first Chern class of the field strength over $\Sigma$ is $m=3$. The 3-sphere supports $j=2$ units of $G_3$ flux and $k=1$ of $H$ flux. In this case the D5-brane carries the same charges as $m=3$ D3-branes which wrap $S^3$ but not $\Sigma$. It also has the same charges as $jm=6$ D-strings and $km=3$ F-strings, which in a supersymmetric background one might expect to form $m\times gcd(j,k)=3$ independent boundstates each of which is a $(k/gcd(j,k),j/gcd(j,k))=(1,2)$-string.
• Figure 5: The First Process: An instantonic NS5-brane bubble wrapping $S$ is spontaneously created and emits a D-string which also wraps $S$. From the perspective of the 6-dimensional worldvolume gauge theory an electrically charged particle/anti-particle pair have been created, wound around $S$ and then annihilated, leaving an electric field. The electric field would prevent the NS5 bubble from collapsing and so the inverse process, emission of an anti D-string wrapping $S$, occurs before the NS5 bubble collapses. In this example the D-string and anti D-string later annihilate. This process conserves D-string charge.