Type IIB Orientifolds without Untwisted Tadpoles, and non-BPS D-branes

TL;DR

The work addresses Type IIB orientifolds engineered to have zero untwisted RR tadpoles but nonzero twisted tadpoles, showing that tadpole cancellation then requires non-supersymmetric brane configurations (including brane–antibrane pairs or non-BPS branes) carrying twisted charge. By constructing explicit six- and four-dimensional models with A- and B-type projections, the authors demonstrate how twisted tadpoles can be canceled without affecting untwisted charges, and analyze phase transitions and stability as internal radii are varied. A key result is that the T^6/Z_4 orientifold without vector structure, previously deemed inconsistent due to uncancellable twisted tadpoles, can be rendered consistent via brane–antibrane cancellation, illustrating the utility of non-BPS branes in tadpole cancellation. The findings highlight a richer landscape of non-supersymmetric, stable vacua and shed light on when brane configurations can compensate for twisted RR charges in compact orientifolds.

Abstract

We discuss the construction of six- and four-dimensional Type IIB orientifolds with vanishing untwisted RR tadpoles, but generically non-zero twisted RR tadpoles. Tadpole cancellation requires the introduction of D-brane systems with zero untwisted RR charge, but non-zero twisted RR charges. We construct explicit models containing branes and antibranes at fixed points of the internal space, or non-BPS branes partially wrapped on it. The models are non-supersymmetric, but are absolutely stable against decay to supersymmetric vacua. For particular values of the compactification radii tachyonic modes may develop, triggering phase transitions between the different types of non-BPS configurations of branes, which we study in detail in a particular example. As an interesting spin-off, we show that the $\IT^6/\IZ_4$ orientifold without vector structure, previously considered inconsistent due to uncancellable twisted tadpoles, can actually be made consistent by introducing a set of brane-antibrane pairs whose twisted charge cancels the problematic tadpole.

Figures (4)

• Figure 1: Configuration of D5- and ${\overline {{\rm D}5}}$-branes in the $\Omega'\alpha$ orientifold of $\bf T^4/\bf Z_2$, for $R_1=1$, $R_2>1$. Discontinuous lines denote strings stretched between D5-branes at $P_1$ and ${\overline {{\rm D}5}}$-branes at $P_2$, which lead to tachyonic modes for $R_1<1$.
• Figure 2: Configuration of ${\widehat{{\rm D}6}}$-branes in the $\Omega'\alpha$ orientifold of $\bf T^4/\bf Z_2$, for $R_1=1$, $R_2>1$.
• Figure 3: Configuration of D7-${\overline {{\rm D}7}}$ pairs in the $\Omega'\alpha$ orientifold of $\bf T^4/\bf Z_2$, for $R_1=1$. The branes wrap the first (shaded) complex plane, and sit at the dot locations in the second.
• Figure 4: Phase diagram for the $\Omega'\alpha$ orientifold of $\bf T^4/\bf Z_2$. For large $R_1$, $R_2$ the stable configuration corresponds to a set of D5- and ${\overline {{\rm D}5}}$-branes at orbifold fixed points. When one of the radii decreases below the critical value $R=1$, brane-antibrane pairs decay into non-BPS ${\widehat{\rm D7}}$-branes, wrapped in the small two-torus and transverse to the large one. For $R_1,\ R_2 \ <1$, the stable configuration contains a set of D9- and ${\overline{\rm D9}}$-branes. When one or two of the radii are exactly equal to the critical value, there exist marginally tachyon-free configurations. For instance, configurations of non-BPS ${\widehat{{\rm D}6}}$-branes partially wrapping a 1-cycle in the first plane, and transverse to the second, for $R_1=1$, $R_2>1$; configurations of non-BPS ${\widehat{\rm D8}}$-branes partially wrapping a 1-cycle in the first plane, and completely wrapped on the second, for $R_1=1$, $R_2<1$; and a configuration of non-BPS ${\widehat{\rm D7}}$-branes wrapping one 1-cycle on each plane for $R_1=1$, $R_2=1$.